Difference of Two Squares

Difference of Two Squares The difference of squares is defined as the product when sum of two numbers is multiplied with their difference. Difference of squares is also known as binomial where both the terms are perfect squares and one term is negative. This rule is not applicable for sum of squares. Symmetrically, the difference of the squares can be factored as following as the like terms get cancelled: (a + b)(a - b) = a^2 ab + ab b^2 = a^2 b^2 The like terms ab and +ab got cancelled. In the above formula, both a and b have to be the same numbers. In other words, the difference of squares is applied only when a and b is same. It is explained with the help of the following illustration: (x + 2)(x 3) = x^2 3x + 2x 6 = x^2 x 6. Now, in the above equation we did not get perfect squares because b was not same and there were no like terms. Now, let us examine when b is same. (x 2)(x + 2) = x^2 + 2x 2x 4 = x^2 4 (now, like terms -2x and +2x got cancelled) Problem 1: Find the factors of the following a. x^2 25 b. 4y2 81 Solution: a. x2 25 = Now we will first try to find out the perfect squares. = We know that x^2 is the perfect square of x = And 25 is the square of 5 = Thus, factors of x^2 25 = (x 5)(x + 5) b. 4y^2 81 = We have recognized the difference of squares in the above equation. Now, we have to find the factors. = 4y^2 is the square of 2y = And 81 is the square of 9 = Thus, factors of 4y^2 81 = (2y 9)(2y + 9) Problem 2:- Find the final product of the following a. (x 7y)(x + 7y) b. (3z 5)(3z + 5) Solution: a. (x 7y)(x + 7y) = x2 + 7xy 7xy 49y2 = x2 49y2 (the like terms got cancelled) b. (3z 5)(3z + 5) = 9z2 15z + 15z 25 = 9z2 25 (the like terms got cancelled)

5 Tips for Improving Your Point of View When Everyone Loves The Boss But Me - Introvert Whisperer

Introvert Whisperer / 5 Tips for Improving Your Point of View When Everyone Loves The Boss But Me - Introvert Whisperer 5 Tips for Improving Your Point of View When Everyone Loves The Boss But Me Just because the boss has a following at work, doesn’t mean you are going to be a follower. You have no idea why your opinion is so different than your peers and that has you scratching your head. The deal is, when you can’t stand the boss; it can make your work life miserable. The great thing about this situation is that you have people around you who see this person differently than you do. All is not lost. You could very likely change your reactions to the boss. The key to this situation is: change. Change can be a tough thing to do particularly when you’re convinced of all of the boss’s flaws and look for daily confirmation that you’re right. We get very invested in our attitudes about people. We think that the boss is the one who needs to change. The reason why it’s got to be you to change is because you are the only one in this equation that you can control. I want to help you accelerate your career by connecting you with your Free Instant Access to my 4 Building Blocks to Relationships eBookâ€" Grab yours by visiting here right now!   Here are some tips for how you can change and improve how you view the boss: 1-Spend some time understanding the behavior the boss has that doesn’t work for you.  This must be actual, observable actions the boss exhibits. All too often when we don’t like someone, we start attributing our beliefs about this person more than true behavior. Spending time getting down to something real is important to solving this problem. 2-Sit down with various people in your group to gain an understanding of what attributes they see in the boss. Ask enough questions so you can hear examples of what they see and how they see the positive qualities in the boss. 3-With a select handful of people you speak to about the bosses attributes, ask them about the observable behaviors that you now better understand. Don’t try to convince them that they shouldn’t like the boss but simply ask them if they see the same things that you do. You may find that these issues are not considered a big deal or that they are of minor concern compared to the positives they see. We all have “warts” so it could be that you are placing much more importance on the flaws than is necessary. 4-Spend time getting to know the boss and the attributes you have learned about from your peers.  Most people tend to avoid a person they don’t like. This does nothing to help you improve your perspectives about this person. Often when we get to know a person better the flaws we once saw become minimized. 5- Check your reactions.  You could be blowing things out of proportion and if that is true for this boss it could be how you react on many things. As a general rule there are very few things that warrant strong, negative feelings and if you have other unlikeable people you know, you may need to seek help so you can put things in their proper proportion. Even if your reactions are mostly narrowed down to the boss, chances are still high that you are over reacting and need to counsel yourself to rethink what and how you react. You may never turn into a fan of the boss. The clue that you can improve from where you are now is in the fact that your peers find value where you don’t. You can learn from your peers and do a great deal to improve your view of this person. You’re not compromising your values. You’re working at gaining insight that you may currently lack.  It’s worth the effort because you spend a lot of your life around the boss and it will improve your outlook. Bottom-line â€" I want to help you accelerate your career â€" to achieve what you want by connecting you with your Free Instant Access to my 4 Building Blocks to Relationships eBookâ€" the backbone to your Networking success and fantastic work relationships. Grab yours by visiting here right now!   Brought to you by Dorothy Tannahill-Moran â€" dedicated to unleash your professional potential.

4 Tips to Manage the College Application Process

4 Tips to Manage the College Application Process Its no secret that the college application process can be quite overwhelming. However, provided you plan ahead and understand what tasks you must complete, you will finish in short order. Take a deep breath and address one aspect at a time. Note all dates and deadlines Perhaps the most critical attribute of the college application process is organization. Submitting an application after its due date is simply not an option, so you must remain informed about approaching deadlines. To do so, create a chart where you clearly record the dates by which all paperwork must be received by your prospective colleges. Remember that the application deadline and the financial aid deadline do not always coincide. Also, note that not all colleges utilize the common application, so you may need to invest additional time into schools that possess unique procedures. This college search tip on how to keep and use a calendarmay be very useful to you as well! Get easier tasks out of the way early The key to mastering the college application process is completing a small portion each day. Finishing an entire application in a single sitting is an impractical plan. Instead, focus on one particular section of the application at a time. Simply filling in personal information such as your name, address, and high school, will make you feel accomplished, and will take even just a little bit off your plate for next time. Just beginning the application at all should relieve a significant amount of stress. Aim to complete these more basic and tedious sections early on before addressing the larger feats, such as the essay(s). Ensure all of your extracurricular accomplishments are well represented A number of students underestimate the importance of the activities section of their resume. The activity resume should be accurate, professional in appearance, and well written. It is in the best interest of prospective college students to maintain an up-to-date activity resume that highlights the defining moments of their high school careers. This resume speaks to admissions counselors about who you are outside of class and how youve spent your extracurricular time throughout high school. Though resumes typically play a minor role in the lives of young students, they are increasingly viewed and utilized in college and beyond. There are many reasons why extracurriculars boost college success! Proofread, proofread, and proofread again! Once youve completed your essays, it is an excellent idea to have an English teacher review them. Your piece may possess grammatical errors of which you werent aware, or one of your points may not have translated neatly on paper. A fresh set of eyes always helps to catch mistakes that you may not discover on your own. Do not overlook the value of having a teacher or tutor edit your essays; a careless mistake, such as writing your instead of youre, can have a detrimental impact on the reader, and therefore on your admissions status. Aside from mechanics, the editor should be able to tell you if the essays are a true representation of you as a person. Both grammar and the overall message you convey to the reader are extremely important. Here are six application essay mistakesthat you want to be sure to avoid. The application essay is an opportunity for you to display your personality, which is not something the application itself usually allows you to do in great detail. Use this oppor tunity wisely!

Derailed Career - Introvert Whisperer

Introvert Whisperer / Derailed Career - Introvert Whisperer Derailed Career? When you get derailed it can mean all sorts of things like a job reassignment or even a demotion.   In other words your career heads in a direction you didn’t plan for or ever think would happen. As you go through your life, your life and career will more or less go in a zigzag pattern.   It never goes in a straight, direct, flawlessly executed manner and setbacks are part of the landscape.   That means that you need to develop the ability to be resilient.   You need to be able to recover from these setbacks so they don’t define you. Understand that resiliency is more than mental toughness â€" although you do need to develop a level of mental toughness â€" you need a recovery plan. Here are my suggestions for a recovery plan: Know it’s going to hurt. A setback will definitely put a dent in your ego.   You may be embarrassed, your feelings hurt and even angry.   That’s ok.   Give yourself a break and feel the disappointment but don’t let it rule your judgment and decision-making.   Avoid reinforcing your hurt by complaining to your co-workers endlessly.   Limit how much you talk about what happened, as it will only make you feel worse. Don’t give up on your goals. Don’t use this situation as a sign that you aren’t up for the task of getting to your goal. Your discouragement at the moment won’t last. Hold off on big decisions. The worst decision you can make is in the aftermath of a setback.   You’re emotional which is fine but you’re probably not in the best shape to make big decisions about your career.   Wait a month or two. Don’t blame. Even if _______ had it out for you, don’t blame what happened on someone else, even if it might be true.   Blaming makes you powerless and you emerge out of your situation feeling unable to guide your career in the direction of your choosing. Don’t be a victim. Regroup and make two goals. You are now in a position not of your choosing. Rather than blow it on this job because you’re acting like a big baby, vow to do so well that they question making the change in the first place.   At the same time, keep your previous career goal. Learn from the experience. Usually, there are good reasons for a move you even if you disagree.   Nevertheless, you need to think about things you could have done better and different so you can use this time to improve your skills.   You need to take another run at the job you had and now that you are wiser due to this experience, you will be better prepared the next time. Rebuild your personal brand. You have work to do to restore the right personal brand.   Don’t just go do this new job.   Think about what traits and impressions you want the management and your peers to have of you.   Be specific without making a laundry list.   Then reinforce these traits each and every day.   Consistency is the key to rebuilding your personal brand.   People will soon forget any gap you may have had. Setbacks happen and they sting.   Don’t let a career derailment define your future. get to you and take the attitude that you will prevail because you can. Go to top Do you know what your next career step is?   Many people don’t. I want to help you accelerate your career by connecting you with your Free Instant Access to my eBook on how to construct your Career SMART Goals â€" that will help you put together your actions and keep you accountable. Get your copy now and start your action plan today! Brought to you by Dorothy Tannahill-Moran â€" dedicated to unleashing your professional potential. Introvert Whisperer

20 English Collocations with BREAK English Lesson via Skype

20 English Collocations with BREAK English Lesson via Skype Hi there. Today were going to look at 20 English collocations with Break.  First of all, lets repeat quickly what is a collocation. A collocation is a specific arrangement of words that has a certain meaning.Are you ready? So lets get started. 20 Collocations with Break BREAK INTO A RUNto start runningExample: When Jenny saw her grandma, she broke into a run.BREAK A HABITto stop doing something that is habit, particularly a bad habit or routineExample: Sarah quit smoking two months ago, she broke a habit shes had for more than half of her life.BREAK THE BANKto cost a lot of moneyExample: This dress is not on sale, but still only £25 full price so it wont exactly break the bank. BREAK EVENto make neither a profit nor a lossExample: The shop hadnt made money since it reopened and well be lucky to break even after it is sold.BREAK FRESH GROUNDto discover something new in the area of knowledgeExample: His work broke fresh ground for performance art.BREAK GROUND WITH SOMETHINGto make a startExample: Were hoping break ground with a brand-new technology.BREAK THE ICEto say or do something that relaxes the atmosphere and make people more friendly towards each otherExample: Sam always knows how to break the ice and get people feeling relaxed.BREAK THE NEWSt o tell someone about something (usually bad) that has just happened which will affect them personallyExample: I crashed Dads car over the weekend but I havent broken the news to him yet.BREAK THE SPELLto spoil something, to bring something special to an endExample: Our eyes met and my heart leapt. Then, she blinked and broke the spell.BREAK A BONEto have a fracture in your bone (arm, leg)Example: She broke a bone in her hand when she fell off the horse. Collocations with Break - Infographic Enjoyed this infographic? Here's what you can do next: BREAK A RECORDto do something better or faster than it has been done beforeExample: Avengers Endgame has broken all the records at the box office.BREAK YOUR HEARTto say or to do something that makes someone feel very sad. To end a relationship with someone by telling them that you are not in love with them anymore  Example: He loved her and she broke his heart by lying to him.BREAK THE RULESto do something that is not allowed by the rulesExample: Its simple, he broke the rules and should be punished accordingly.BREAK A WINDOWto make a crack in the windowExample: Somebody broke the window last night.BREAK THE SILENCEto end a silent period by starting talking or making noiseExample: I broke the silence by saying something silly about the weather.BREAK IN TWOto break something in two partsExample: She broke it in two and gave me half to eat.  BREAK YOUR BACKto put a lot of effort into achieving somethingExample: I was breaking my back doing this stinking job.BREAK THE BACK OFto complete the hardest or main part of an exercise, project, assignment, etcExample: Today, they finally broke the back of this tricky composition.BREAK YOUR FALLto stop someone from falling downExample: The falling man landed directly on top of the donkey, which broke his fall.BREAK A CODEto figure out a secret code so that you are able to read the messageExample: We broke the secret code yesterday. By accident, almost.

ACT How to Make your Own Study Schedule

Preparing for the SAT/ACT How to Make your Own Study Schedule ACT SAT Prep and College Admissions Blog No matter how many times your parents have repeated it to you, it never quite sinks in â€" If you fail to plan you plan to fail. While this feels a bit dramatic, in a test like the SAT or ACT it is important to realize that preparation can have a significant benefit on your score and on opportunities that stem from this such as college admission and scholarships. While many students have performed well in high school, standardized admissions tests can be a limiting factor because students often fall into a few common traps, such as the idea that being a good student translates directly into a high performing standardized test taker. While this may be true for some students, it often is not the case. College admissions exams often require knowledge on how to study for and take a standardized exam. The best way to overcome this hurdle is by creating a study schedule and planning for test day ahead of time. Step #1: Set Your Target Score While it can be daunting to make a list of schools this early in the process of college applications, this will make setting a goal much easier. The advice I typically give to students is to create a list of schools with three categories â€" dream schools or reach schools, mid-tier schools, and safety schools. It is also important to look at what each school is available to offer based on your desired career path or the ability to explore if you are unsure at this stage of your life. After establishing your list, use the internet to find published SAT and ACT scores for each school. I recommend looking at the seventy-fifth percentile and the twenty-fifth percentile of each school. Your goal score should be the highest seventy-fifth percentile score among schools on your list. In doing so, you’ve placed yourself in the top twenty-five percent of applicants for standardized testing scores. This is the score that would likely allow your college application to be reviewed at any school on your list. It is also important to note whether your school requires the essay portion as this will impact your testing registration. Although, I strongly advise taking the essay portion of the exam whether it is required or not as it is another easy opportunity to evidence your strong scholastic abilities. Step #2: Take a Practice Exam Taking a practice exam will allow you to determine your baseline SAT or ACT performance. This will help determine how much time you will need in test preparation. It is also an opportunity to familiarize yourself with the test prior to taking the real SAT or ACT. Both tests have official published practice exams that are arguably the closest to the official exam in terms of test questions and structure. When taking your practice exam, it is crucial to try to recreate the testing environment as closely as possible. This means taking the test under timed conditions, at a similar time of day as the real test, no electronic use during or in between sections, and finding a quiet location. This will allow you to obtain the most useful diagnostic score and to set goals for your test preparation. After taking your practice exam, compare your target score to your baseline exam score. Determine the point difference between these two scores. Do not get discouraged by this portion of test preparation, the SAT and ACT are both tests that you can learn to take. A lot of the preparation for the SAT and ACT requires understanding how the test is set up and being comfortable with the timing of the test. The SAT is split into Reading (52 questions in 65 minutes), Writing and Language (44 questions in 35 minutes), Math (58 questions in 80 minutes), and the optional essay (one essay in 50 minutes). The ACT is composed of five sections: English (75 questions in 45 minutes), Mathematics (60 questions in 60 minutes), Reading (40 questions in 35 minutes), Science (40 questions in 35 minutes), and Writing (1 essay in 40 minutes). As you can see, these sections are short, and it is imperative to know how much time to spend on each question in order to complete the section within the allotted t ime frame. Step #3: Pick a Date Most students will schedule the SAT or ACT for the spring of their junior year so that there is time to retake the test the following fall if needed. There are a number of factors that go into picking a date. First and foremost, you should determine the latest date that allows you to have a score prior to submitting your application to schools. This should be your last chance date, the date that you need to take your test by in order to apply for college. Some students take the SAT or ACT a second time to see a score increase. If adequately prepared, you likely will not need to take the test again barring any events like getting sick or have another emergency come up around your test date. Another factor to consider is how much time you will need to prepare in order to attain enough knowledge and practice to achieve your target score. For a student who needs to improve their score by 0 â€" 100 points you may need about 30 hours of preparation. Whereas a student who has a larger improvement in the range of 100-300 points may need closer to 100 hours of preparation. It is important to be realistic about your schedule as a student and other commitments. For example, if you are in band during marching season, this might not be the best time to schedule the SAT or ACT because most of your weeknights and weekends are occupied with extracurricular activities. The best way to determine how much time you have to study for the SAT and ACT is to write out a typical schedule for the week of your mandatory school activities, extracurricular activities, job, time needed to study for class, or any other commitments. The remaining time that is left on your schedule, beyond sleeping an d eating could feasibly go towards your SAT or ACT preparation. However, it is important to balance your schedule. Working too many hours on academic pursuits could lead to exhaustion that will impact your test performance. After taking these factors into consideration, it is important to go online and schedule your exam early. This will keep your testing costs to a minimum and ensure that a spot is reserved for you on test day. Step #4: Find Study Materials That Work for You In preparing for the SAT or ACT, reflect back on the methods that lead you to score well on exams in the past. Did you do well in a big study group? Using practice exams provided by a teacher or that you found online? Do you enjoy studying with outlines or flash cards? A number of study resources have been published for the SAT and ACT. Blog articles written by reputable sites can even provide helpful and free tips, like this one from Brainly about effective SAT essay strategies. These resources range in application and work differently for each student. The best study resource is the one you will actually use and even enjoy at times. It is crucial to take many practice passages and exams to gain familiarity with the test itself. It is also important to spend time reviewing these passages and tests. This is where you will find the common patterns and mistakes you’re making and allow yourself the greatest room for improvement. This is the single biggest mistake I have seen amongst a ll standardized test takers that is so easily corrected. Step #5: Setting a Schedule After selecting your study resource, it is time to sit down with a calendar and divide up your workload for your study period. It is important that you work consistently towards your goal, taking a break once or twice a week as needed. This will build up your stamina for test day. When you divide up your work set realistic goals on how many pages you can read or passages you can take in the amount of time you have each day to work on your SAT or ACT. Establish goals throughout your test preparation for score improvements so that you can assess whether you are set to achieve your goal. These checkpoints will give you an idea of whether you need to reschedule your exam and will keep you from cramming for the exam. When setting up your schedule, it can be tempting to only focus on the sections that you find are weakest based on your diagnostic exam. While you should spend more time on these sections if there is a significant difference in your section scores, it is important that you have a balanced score among your sections on your exam. Make sure that you allot time to study all sections of the exam as a balanced score is often reflective of an academically well rounded student. Step #6: Take the Exam Now that you have studied hard, it is time to take your exam. Make sure you are well rested the week leading up to your exam. Trust the hard work you have put into this process and enjoy the challenge. Best of luck! About the Author Jordan Salley is a senior ACT and SAT tutor for MyGuru. For more information on ACT and SAT prep, our unique approach, and our tutors, visit us here for ACT prep or here for SAT prep.

Win $15,000 for Innovative Visual and Oral Health Solutions

Win $15,000 for Innovative Visual and Oral Health Solutions http://mms.businesswire.com Whole You, Inc.,  a Mitsui Chemicals company committed to offering solutions that allow those with sensory and physical mobility challenges to live life to the fullest, has teamed up with crowd-sourcing company InnoCentive to challenge healthcare professionals and the public to create innovative solutions for those with oral and visual challenges, according to this press release. On the oral side of the challenge, Whole You is looking for ways to motivate patients and incentivize their compliance to regularly use their oral appliances to effectively manage obstructive sleep apnea. On the visual front, the company is asking for ideas about other services that vision care providers can offer to optimize a persons health and well-being. The person that recommends the best idea in each category will be awarded $15,000, an amount I know any college student needs. In addition, Whole You announced its advisory group in the press release, which consists of professionals with expertise in both sensory and physical mobility areas. This group will provide input and guidance into the development of Whole Yous innovation efforts and will judge the Whole You challenge submissions. http://eye.uams.edu Here is a list of the current group: • Rupa Balachandran PhD., CCC-A Program Director Audiology, Associate Professor Department of Speech Pathology and Audiology, University of the Pacific • Dr. Ting-Ling Chang, DDS, Clinical Professor and Section Chair of Prosthodontics at the Division of Advanced Prosthodontics, UCLA School of Dentistry • David Green, Social Entrepreneur, MacArthur Fellow and Ashoka Fellow • Dr. Moshe Lewis, MD, MPH, Chief, Department of Physical Medicine and Rehab, California Pacific Medical Center, St. Luke’s Campus • Dr. Katayoun Omrani, DDS Orofacial Pain specialist, Los Angeles Pain Clinic; Dentist at the Headache, Orofacial Pain and Sleep Apnea Program at the Cedars-Sinai Pain Center • Dr. Frank Spors, MS, PhD, Assistant Professor at the College of Optometry at Western University of Health Sciences “We have identified many sensory and physical mobility challenges that individuals face and believe that an open innovation approach is essential to creating truly ground-breaking products that we know the market needs,” said Hiromi Inagaki, chief innovation officer, Whole You. “The partnerships with our advisory group and InnoCentive demonstrate our commitment to tapping in to great minds that are aligned with our vision â€" to deliver innovative solutions to for those with sensory and physical mobility challenges.” The entirety of Whole Yous partnerships and collaborations, including the open innovation challenges and expanding advisory group, will be a part of Whole Yous Living Lab, which is a unique, interdisciplinary innovation network where a broad range of experts come together to develop solutions to optimize health and well-being. https://thenypost.files.wordpress.com “One of my main goals is to provide my patients with the best solutions available so they can live life to the fullest, and Whole You is now on the frontline of this innovation,” said Dr. Ting-Ling Chang, DDS, Clinical Professor and Section Chair of Prosthodontics at the Division of Advanced Prosthodontics, UCLA School of Dentistry. “I am pleased to be a part of the company’s platform that encourages ongoing discussion that will drive enhancements in the dental industry. I look forward to seeing what solutions will come from the InnoCentive challenge.” Submit your oral or visual solution to one of the InnoCentive challenges here. For more information about Whole You, click here.