What Is Isotope in Chemistry?

What Is Isotope in Chemistry?What is an isotope in chemistry? Isotopes are the different types of chemical elements. You will come across these in our everyday life such as oxygen, calcium, lead, uranium and of course mercury, which are the most toxic chemical element.These elements are all stable and not in their own makeup and they don't have any interaction with other element. What is an isotope in chemistry? In science there are a couple of substances that have different mass numbers.Isotope in chemistry is the development of isotopes. This means one element can exchange one of its atomic number with another element. Isotopes exist when two similar atoms, or nuclei, of atoms with different atomic number 'bump' into each other. The bump then flips the atomic number by one or more times, which result in the isotope.Since the isotopes are similar with each other the atoms will have the same elemental element. The atoms will get thrown out of the atom.So, what is the isotope in chemi stry is all about how different elements react to each other. Since the atoms in the atoms with the bump each have a different atomic number, the atomic mass will be different. So, the atoms that are bumping against each other will be different from the original atoms. The same thing happens with atoms that are opposite each other.Isotope in chemistry also relates to radioactive elements. Isotopes are unstable and this is the reason why they can become radioactive. When an isotope is made in the laboratory it's unstable and this means that it doesn't stick to other atoms easily. They get stuck to the surfaces and they make a gas that can be seen. Uranium, thorium and America are the three types of isotopes. Uranium and thorium are unstable and America are stable. The America is used in America.Isotope in chemistry, also known as a stable isotope, is very useful in making the anti-cancer drugs that are so important in fighting cancers. The isotopes are called isotope in chemistry bec ause they change in mass and they don't change their chemical composition. If you need to know more about isotope in chemistry, go online and find out more.

Chevron Refinery Fire West Coast Gas Prices Soar In Wake of Shutdown

Chevron Refinery Fire West Coast Gas Prices Soar In Wake of Shutdown The Richmond refinery as crews attempt to squelch the fire, courtsey of MSNBC.com This cataclysmic image was seen by residents of the Richmond area, a suburb of San Francisco, after the horrendous explosion and subsequent Chevron refinery fire that  sent plumes of smoke over the area. The fire erupted Monday evening in the massive refinery until it was put out early Tuesday, but the entire west coast of the United States will feel the effects of this catastrophe for weeks, if not months, in their wallets. Huffington Post San Francisco has been covering this story very closely, and according to their reports,  they got chief oil analyst at Oil Price Information Service Tom Kloza to comment about how the  Richmond Chevron refinery is particularly big and important to the West Coast market,    produc[ing] about 150,000 barrels of gasoline a day â€" 16 percent of the regions daily gasoline consumption of 963,000 barrels. The potential for this disaster to be worse than the BP Oil Spill is limited, as fire crews have already subdued the blaze. However, thousands of residents that live within very close proximity to the refinery are complaining about health problems. Lawsuits will definitely be on the horizon and Chevron could be on the hook for millions of dollars if it is found that a lack of oversight caused the explosion. The official statement from Chevron was released through the San Franicisco Gate newspaper, and you can follow all of Chevrons updates at their website:  http://richmond.chevron.com/home/news/incidentresponse.aspx. The Gate newspaper reported that Chevron will not speculate on the cause of this incident. [The] priority right now is containing the fire and protecting the health and safety of our employees and  community. Jason Dearen of the Associated Press explained how West Coast gas prices could skyrocket in result of this loss of oil production.  Already, the  average price of regular gasoline jumped in California from $3.86 a gallon on Tuesday to $3.94 on Thursday. Dearen reports that some experts expect the disruption in production to last for weeks and push prices beyond $4 a gallon. The Richmond refinery makes upwards of 200,000 barrels per day,  accounting  for one-eighth of Californias refining capacity. Shipping to Washington, Oregon, Nevada and Idaho, expect gas prices to bolt upwards in the next few days. Especially with the summer months creating a spike in American mileage, that will put a strain on Americans young and old. Most importantly, as Dearen found out via Rayola Dougher,  a senior economic adviser with the American Petroleum Institute. California has the cleanest burning gas in the nation, so this is definitely a market disruption. Therefore,  California can’t replace those supplies with imports from Washington state, Asia and the Gulf Coast, so it’s more difficult to ease the impact of the lost production. California, already dealing with rolling blackouts due to the excessive heat, are going to have to conserve at unprecedented rates in order to ride this blaze out and not break the bank.

Soaring Imagination Fuels This Young Writers Creativity

Soaring Imagination Fuels This Young Writer’s Creativity Soaring Imagination Fuels This Young Writer’s Creativity Morgan, 11-years-old, Math Level J Reading Level HII With an imagination that soars, 11-year-old Morgan allows her creativity to run wild in just about anything she does. One of Morgan’s biggest strengths is her determination to reach her dreams. And her secret to reaching her dreams? Setting goals.   “I have always been told that I am very determined for my age,” said Morgan. “One of the things I am proud of is when I set a goal for myself, I remain determined to reach my goals. I like thinking independently and I take responsibility for my education. I believe this is a skill I will use my whole life.” One of Morgan’s creative outlets is writing. For inspiration on her pieces, she turns to the experts. Morgan is fascinated by the work of film directors and writers. She loves to hear how they develop characters, scripts, and other decisions that are made when making a film. “I really enjoy playing as my imagination allows,” said Morgan. “I enjoy thinking up stories and developing characters for those stories and writing short stories on various topics! Despite balancing a busy schedule, Morgan finds the time to give back through volunteering. Morgan and her sister started a donation site to raise awareness and funds for Sole Hope. This non-profit organization’s mission is to fight parasitic insects in Africa and provide treatment for those infected. Morgan’s efforts were able to impact 200 lives. Morgan was one of 56 students selected for Kumon’s 3rd Annual Student Conference in Chicago, Illinois. “Here I am, 11-years-old, and we’re staying in downtown Chicago because of my hard work in Kumon. It was such an amazing feeling,” said Morgan. “I felt like a celebrity when I walked in! I loved listening to the speakers and getting to work with other Kumon Students! My biggest question at the end was, can I do this again next year?” Morgan shares with us who her inspiration is and plans for the future. What do you enjoy most about Kumon? I truly enjoy being able to complete my math assignments quickly in school. I’m now able to help my friends solve and understand challenging math concepts. How has Kumon helped you academically? I’ve learned to remain disciplined. Kumon reminds me of the importance of sticking with something until it’s complete. Little by little and bit by bit, if I am disciplined, I know I can accomplish great things. I find if I consistently apply myself, I can make progress in other areas like biology and creative writing. How has Kumon helped you outside of the classroom? As I look back at everything I’ve accomplished in Kumon, I can see that with consistent effort over time, I can overcome challenges and accomplish amazing things. I’m realizing that this is true in life as well. What do you want to be when you grow up? There are so many things I want to do when I grow up. I aspire to be an inventor, a medical research doctor, a micro-biologist, and much more. I figure I can do all of these things during my life! Who’s your biggest inspiration and why? My biggest inspiration is the great mathematician, Katherine Johnson. She was incredibly instrumental in helping NASA put a man in space, and safely bring him back to earth. She definitely has math superpowers! Katherine even received the Presidential Medal of Freedom from former President Barack Obama, which is the highest civilian honor in the United States. What advice would you give to kids just starting Kumon? Focus on today’s work and don’t worry about tomorrow’s or the rest of the week. If you get stuck, take a short break to clear your mind, then get back to it. When you finish, celebrate another completed day. Discover even more student success stories. You might also be interested in: Encourage Creativity and Imagination through the World of Poetry Young Pianist Proves Practice Makes Perfect Young Basketball Star is Shooting for the WNBA This Young Hockey Player is Making Strides On and Off The Ice Soaring Imagination Fuels This Young Writer’s Creativity Soaring Imagination Fuels This Young Writer’s Creativity Morgan, 11-years-old, Math Level J Reading Level HII With an imagination that soars, 11-year-old Morgan allows her creativity to run wild in just about anything she does. One of Morgan’s biggest strengths is her determination to reach her dreams. And her secret to reaching her dreams? Setting goals.   “I have always been told that I am very determined for my age,” said Morgan. “One of the things I am proud of is when I set a goal for myself, I remain determined to reach my goals. I like thinking independently and I take responsibility for my education. I believe this is a skill I will use my whole life.” One of Morgan’s creative outlets is writing. For inspiration on her pieces, she turns to the experts. Morgan is fascinated by the work of film directors and writers. She loves to hear how they develop characters, scripts, and other decisions that are made when making a film. “I really enjoy playing as my imagination allows,” said Morgan. “I enjoy thinking up stories and developing characters for those stories and writing short stories on various topics! Despite balancing a busy schedule, Morgan finds the time to give back through volunteering. Morgan and her sister started a donation site to raise awareness and funds for Sole Hope. This non-profit organization’s mission is to fight parasitic insects in Africa and provide treatment for those infected. Morgan’s efforts were able to impact 200 lives. Morgan was one of 56 students selected for Kumon’s 3rd Annual Student Conference in Chicago, Illinois. “Here I am, 11-years-old, and we’re staying in downtown Chicago because of my hard work in Kumon. It was such an amazing feeling,” said Morgan. “I felt like a celebrity when I walked in! I loved listening to the speakers and getting to work with other Kumon Students! My biggest question at the end was, can I do this again next year?” Morgan shares with us who her inspiration is and plans for the future. What do you enjoy most about Kumon? I truly enjoy being able to complete my math assignments quickly in school. I’m now able to help my friends solve and understand challenging math concepts. How has Kumon helped you academically? I’ve learned to remain disciplined. Kumon reminds me of the importance of sticking with something until it’s complete. Little by little and bit by bit, if I am disciplined, I know I can accomplish great things. I find if I consistently apply myself, I can make progress in other areas like biology and creative writing. How has Kumon helped you outside of the classroom? As I look back at everything I’ve accomplished in Kumon, I can see that with consistent effort over time, I can overcome challenges and accomplish amazing things. I’m realizing that this is true in life as well. What do you want to be when you grow up? There are so many things I want to do when I grow up. I aspire to be an inventor, a medical research doctor, a micro-biologist, and much more. I figure I can do all of these things during my life! Who’s your biggest inspiration and why? My biggest inspiration is the great mathematician, Katherine Johnson. She was incredibly instrumental in helping NASA put a man in space, and safely bring him back to earth. She definitely has math superpowers! Katherine even received the Presidential Medal of Freedom from former President Barack Obama, which is the highest civilian honor in the United States. What advice would you give to kids just starting Kumon? Focus on today’s work and don’t worry about tomorrow’s or the rest of the week. If you get stuck, take a short break to clear your mind, then get back to it. When you finish, celebrate another completed day. Discover even more student success stories. You might also be interested in: Encourage Creativity and Imagination through the World of Poetry Young Pianist Proves Practice Makes Perfect Young Basketball Star is Shooting for the WNBA This Young Hockey Player is Making Strides On and Off The Ice

10 Reasons to Invest in Foreign Aid

10 Reasons to Invest in Foreign Aid via Pixabay 4. Foreign aid facilitates global connections. Africa is nearing one billion mobile subscriptions, and  Project Loon  is providing WiFi with tennis court-sized balloons. Development goals in several countries look to increase total global connectedness to the internet, which means access to healthcare information and job sites as well as social media. 5. Foreign aid inspires innovation.   American tech company initiatives, such as  4Afrika  by Microsoft, fund local tech start-ups. For example, the Cardiopad, a touchpad device for heart exams and a breakthrough in medical technology, was invented in Cameroon. 6. Foreign aid helps the environment. The connection between global poverty and carbon dioxide emissions may not be obvious at first, but diversification of energy sources means new jobs and resources for everyone. As the global economy grows, emissions  go down. 7. Foreign aid promotes equality for women. More women are running for officeâ€"and  winning seatsâ€"than ever before. Reducing poverty through donations to foreign aid offers women access to education and healthcare, improving their financial and social independence. via Pixabay 8. Foreign aid helps stabilize states in conflict.   A 2017  study  published in the Global Health Journal found that “The highest quartile of US health aid per capita spending was associated with a large and immediate decline in the level of state fragility.” This means that places with more humanitarian aid are less likely to erupt with violence and collapse, making a safer place for everyone. 9. Foreign aid hinders the influence of terrorist groups.   Groups like ISIS are successful in poorer regions, incentivizing new recruits with the promise of resources. If foreign aid provides resources to these regions first, terrorist groups suffer a major blow to their campaign of fear. As U.S. Senator  Lindsey Graham  (R-SC) said in a 2017 argument for funding foreign aid programs, “The worst nightmare for al Qaeda is to come into a community that feels supported and has hope.” 10. Foreign aid has a chance to produce a direct return. A charitable donation to a foreign aid organization with 501(c)(3) status is claimable on tax returns. Buying stock in Kroger is not.

Making Money by Tutoring Kids in the Classroom

Making Money by Tutoring Kids in the ClassroomTutoring kids is an extremely effective way to make money by tutoring them in the classroom. Many people have tried this at home, but it is still very much a new field. The problem is that most people are not familiar with how to make this business profitable.Yes, you can tutor people online, and yes, you can make a great deal of money. The issue is that a lot of it depends on how easy the simple stuff is to do. It is certainly easy enough to tutor the little ones in the elementary school level, but they have very different learning styles than the elementary students. Most of these elementary students have really big books and need lots of reading time.You will have no luck tutoring elementary schools at all, because they will be constantly breaking up the work and turning it into small pieces to take care of. Once they have the first-grade work done, they will expect the students to come in and tutor them. The real focus in this part of the teaching profession is teaching the big books.People who have made a good living tutoring adults at elementary school levels will tell you that there is no real reason to tutor little children at this level of education. They will not take the time to learn anything new, and there is no real point in trying to teach them how to read. Even if you have great English speaking skills, as most people who do this have, this is still a language that needs to be learned at a very young age.The second-grade level is where most people's tutor, because their students have never heard anything about how to read and write, and will be learning this stuff at a very early age. This is the stage when the child's vocabulary and composition skills are being developed. The second-grade students will most likely never go beyond this level of education. Most of their basic reading and writing skills will be at the end of the first year of school.Once your students graduate from this level, it will be very difficult for you to make money tutoring them. Remember, most of the people who tutor children at this level are being paid by private schools to do so. At this point, it is much harder to find a school willing to pay more than the federal minimum wage for a full time salary teacher. This is why the best thing you can do is find a good state school, and begin tutoring your children early.As the children start out in the educational level, they will have the most time to develop reading and writing skills. So you will find that your tutoring income increases as you teach the younger children, and the older ones also pick up the language. At this point, if you are looking for a way to make money by tutoring, start tutoring at the right level, and you will be in good shape.

What to Look For in Private Tutoring

What to Look For in Private TutoringIn the United States, there are many private tutoring services in operation that provide tutoring services to children of all ages. The school tutors are skilled and capable of providing excellent tutoring services to students of any age. However, when parents find that their child is having problems with his or her studies, they may consider seeking the assistance of a tutor in the form of a private tutor in the United States.Although these tutors are usually paid for the school lessons, it is not necessary for the students to pay the tuition fees of the tutors. In fact, these services are really beneficial for parents. This is because such private tutoring services are always willing to accept any parents who would like to pay for their tuition fee.There are numerous companies in the US that offer tutoring services to students of all ages. In fact, the students of this kind of services are mostly from very poor backgrounds. Therefore, they have l ess to lose and therefore can afford the services of a tutor. Another advantage of paying for a private tutor is that you do not have to bear all the expenses as a student is reimbursed in full.You have a wide variety of companies providing tutoring services in the United States. However, you should try to look for those which are most qualified to offer tutoring services to students. There are certain things that you should be aware of before deciding to seek out tutoring services from a company in the United States.You should ensure that you do not sign up for a company which offers tutoring services to children who live far away from your area. This can often affect your quality of life because you would be required to travel quite a distance to attend a private tutoring session. On the other hand, you should also make sure that the tutoring services are conducted by experienced tutors and not bysomeone who have only been in this field for a short time. If you are aware of the fa ct that you have to pay a portion of the tuition fee as well, you should seriously check the credentials of the tutor. You can check the course syllabus and the previous work experience of the tutor.You should also make sure that the tutor uses a computer and has passed an aptitude test. You can go online and check the net for some other sources for a tutor. You can also visit your local business or a bookshop to see if the tutor is certified by the tutoring agencies. You can also look for reviews about the tutors in the net.Tutoring services provided by tutoring agencies can also be highly beneficial for the students. These services are free from all the costs and expenses, which can hinder the students in getting to their studies. It can also help the students in improving their school marks as the tutor is an expert in delivering quality educational sessions to the students.

A Brief Linguistic History of Russia

A Brief Linguistic History of Russia History of the Russian Language ChaptersThe ethnic origins of the RussiansThe melting pot of Slavic languages and the rise of Old RussianThe Cyrillic Alphabet…and the Russian oneRussian language and religionClassical Russian LiteratureThe Russian speaking world in the 21st centuryAlthough American-Russian relations aren’t in a particularly rosy place, more and more American students are once again choosing to study the language of Tolstoy.St. Petersburg has become a popular cultural destination, and the number of international marriages is on the rise.The Russian language (???????) is very different from English and Romance languages in general.To a Westerner listening to a Russian, the language usually leaves an impression of sweetness, warmth, and a singsong tone.Russian is also associated with an accent that, in French as in English, remains particularly touching and charming. At least when it is delivered in a feminine accent, the filmmakers seem to think it creates a femme fatale!Russian grammar isn’t ve ry easy. Russian uses a lot of prefixes, suffixes, different endings, and vowel shifts.But isn’t Russian just so cheerful and pleasant to listen to? (Despite the fact it’s coupled with a baffling alphabet - just like Arabic - but looks like a work of art?)In this article, we will go back through the centuries to follow developments in Russian linguistics step by step... And discover Russia as it should!Central Russian, a mix of the other two dialectsSouthern Russian, wetter, fricative and less accentuated.All good things to study before traveling to Russia! With all this new information, searching for Russian language course London  produces the best internet results but find the best local  Russian teacher  on Superprof.Discover the formalities to obtain a visa for Russia …

Useful Tips That Can Help introverts to score a promotion - Introvert Whisperer

Introvert Whisperer / Useful Tips That Can Help introverts to score a promotion - Introvert Whisperer Useful Tips That Can Help introverts to score a promotion Fear of anything affects your progress. If you think you are an introvert and want a good move in your career, you need to focus on one-on-one relationships at your office premises. Author of the best-selling book “Quiet: The Power of Introverts in a World That Can’t Stop Talking” Susan Cain says that the culture having outgoing and uninhibited values make it difficult for an introvert to manage especially in the workplace. As per her, many skills of introverts depend on the way of their interactions with others on a personal level. If they want to achieve a successful career, introverted employees should use this ability to catch senior-level roles. A study reveals that more than half of CEOs, who achieved better than expected were introverts. Let’s discuss some tips to achieve a promotion if you are considering yourself as an introvert. 1. Choose a career that suits your strengths Your comfortableness makes your work easy to do. If you are not enjoying your work or you have totally different aspects of your work which doesn’t suit your skill, you may face difficulties to continue your work. Always go with your skills and strength for pursuing a better career in your life. Forbes has disclosed a list of the most introvert-friendly careers that including animal care, service workers, court reporters, archivists, and social media managers.  Trade Schools also share this list that distinguished the jobs as per the different types of introverts based on social activities, level of thinking, or anxious. What do you think that being an introvert you can’t be successful in any field? It is not true! You need to make some adjustments to be successful. We can change our persona up to a level and beyond a point, you will start to lose your individuality. Bill Gates and Bill Clinton can’t be the same person with the same reflection. No matter how much they polish their skills and add values in their personalities. 2. Make a network that makes you comfortable An introvert is someone who tends to rejuvenate best through alone time.   In other words, an introvert doesn’t incline to attend lunch and every happy hour, and optional professional development opportunity. But that doesn’t imply that they have to miss career-boosting advantages of active networking. This point reflects that you need to actively participate in every form of communication. Proper your relationships (either personal or professional) as per your ways. To be the part of active networking, choose a format that doesn’t bother you to make regular check-in on your work contacts with real conversations on important events and interests such as email, messaging apps or LinkedIn. If you feel more comfortable in small social activity than events, then skip the large group gathering. Pay more attention to meetings with people you’re interested in building a relationship. This will give you more powerful networking rather than spending much time with larger numbers of people. 3. Makes notes for better communication If you don’t speak out what you need or want, you will never have what you want. When if you want to avoid excess attention, then imposter syndrome  and introversion can go hand to hand. This can allow you to provide excellent and promotion-worthy work that you never quite step up to take appreciation for. This will also let you generate great ideas that you don’t disclose during meetings. If you want to express your ideas and get credit in person, you know you will go blank once everyone’s focus on you, then have some backup with yourself. While attending any meeting, make notes on what you have and what you want to share. Also, refer to these notes when you choose to speak up. It will help you to introduce your contribution that makes sure you’re not thinking on your feet and concentrating on what is happening around. Be confident while sharing your thoughts on something important and don’t forget to make a note before speaking anything. 4. Don’t forget to learn Try to move beyond your job narrative to widen your knowledge base. Take a stand on the things in which you find yourself confident and comfortable. To expand your learning, you need to add new skills to your persona. If you want to get promoted, you have to show something different from others. Same this is said by Dorie Clark, marketing strategist and author of  â€œStand Out: How to Find Your Breakthrough Idea and Build a Following Around It.” Clark suggests that people require to spend your time in innovations and experiments to enhance your skills. Try some different duties or start some new things that offer you some independence and creativity to get noticed. If you consider yourself an introvert, take the classes on an unfamiliar area or try to search for a solution that addresses a problem within your company. It is just like if you need assistance to work on your assignments, don’t hesitate to take assignment help online services from experts. 5. Take the help of a mentor All know the work environment of offices and politics which we face during various activities. Indeed, your relations can generate or break your chance to be considered for a promotion. Being an introvert, if you avoid making large groups of work friends as your close associates, then promotion becomes hard to get within a company unless those close relationships include more senior employees who are keen to mentor you and take care of your career. It may difficult to get the right approach for finding the right mentor, but it is as important as making a friend who interested in your promotion. A relationship with a mentor helps you to grow as a professional with someone to witness that development and promote you to achieve higher levels of responsibility. In fact, your mentor can support you and advise you to perform better on your projects. If you’re an introvert and hard worker, then you would be one of such people J.K. Rowling, Shonda Rhimes, and Michael Jordan. It doesn’t matter that you are introvert or not, your effort and performance will give you the credit of your work. 6. Be ready for a no The word “No may be the hardest words you’ll ever hear in any kind of conversation. Usually, when you hear a no, your spiral power gets down and you start to doubt your qualities. You assume that “you didn’t deserve it” or “you are not good enough.” It may not easy to overcome this situation but don’t get quiet. Despite sitting, get curious and ask why not you. Analyze your output and talk to your senior. It all depends on the answers to your boss. He will let you know the reasons for getting the answer “no.” It may possible that your company doesn’t have enough budget and may have some other reasons. But if you don’t raise questions, you will never have the reason of “No.” Once you get the discussion with your boss and get the answer to your queries, time to decide whether you want to stay or go for another organization. Author bio: Kaylee Brown a professional blogger who has more than 6 years’ experience in content creation. Currently, she associated with EduMagnate provides online assignment help to all needy students. Contact her at any time to get proper support of assignment writing. Go to top Let me emphasize that Self-Promotion doesn’t have to be obnoxious to be effective.   But, if you don’t Self-Promote you, who will? If you ever want to get ahead, you have to learn how to Self-Promote. I want to help you accelerate your career by connecting you with your Free Instant Access to my video that shows you simple, yet effective ways to Self-Promote. Start watching now by clicking here! Brought to you by Dorothy Tannahill-Moran â€" dedicated to unleashing your professional potential. Introvert Whisperer

Online Algebra 1 Practice Tutors - Algebra 1 Tutors

Online Algebra 1 Practice Tutors - Algebra 1 Tutors H.C.F. (Highest common factor) and L.C.M. (Lowest common factor) is the part of algebra 1. Methods to solve H.C.F and L.C.M.: - Division method Factorization method. Lets practice few problems of algebra 1:- Example: - Find out the L.C.M. and H.C.F. by factorization i) X^2 + x, x^3 x ii) X^3 + 2 x^2, x^3 + 3 x^2 + 2 x Solution: - i) 1st expression = x^2 + x = x ( x + 1) 2nd expression = x^3 x = x ( x^2 -1) = x (x + 1) (x 1) The common factors of the two expressions are x and (x +1). Therefore H.C.F. = x (x + 1) (x 1) is the extra factor in the 2nd expression. Hence the required L.C.M. = x (x + 1) (x 1) ii) 1st expression = x^3 + 2 x^2= x^2 (x + 2) = x * x * ( x +2) 2nd expression = x^3 + 3 x^2 + 2 x = x(x^2+3x+ 2)=x (x^2 + 2 x + x + 2) =x {x ( x + 2 ) + 1 ( x + 2 )} =x (x + 2) (x + 1) In both the expressions, the common factors are x and x + 2 Therefor H.C.F. = x (x + 2) The extra factors are x in the 1st expression and x + 1 in the 2nd expression. Therefore L.C.M. = x ( x + 2) x (x + 1) = x^2 (x+1)(x+2)