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Binomial Expansions Reflection By: Arsalaan Muhammad Math: Mrs. Taher Click to continue rule for expanding binomials These are 2 generalized expressions: (a+b)2 = a2 + 2ab + b2 and: (a-b)2 = a2 -2ab + b2 Click to continue The Equation we looked at In the investigation 2 (0.99) = (1-0.01) (1-0.01) = 2 1 - 2 x 1 x 0.01 + 0.012 Click to continue Today vs. The “Bad old days.” Today, we have calculators which perform complex numerical calculations easily. This takes just seconds to do. Before calculators, scientists, mathematicians as well as other people had to use a pencil and paper to create or solve their equations. It could take people a while to solve their equations on paper. Some of the smartest people ever wrote every equation down the old fashion way. Click to continue Binomial expansions VS. Long Multiplication Binomial Number: It is more efficient to use binomial numbers when the question is more complex. It helps show what steps you are taking to get to your answer.If you use binomial numbers to solve an equation where you have to multiply numbers by more than 3 digits, then, it would take a long time as you have to keep adding a co-efficient. Long Multiplication: Generally, long multiplication is much easier as all you have to do is multiply the numbers and add. At times, using long multiplication can be hectic. For example, if you multiply 5 digit numbers by numbers with more digits, then, it will become time consuming. If you make a simple addition mistake when trying to find the answer, you will have to go through the entire process of how you got the answer to find your mistake. Click to How our method can help an engineer from 100 years ago solve an equation faster Their complex equations can easily be solved as this method helps to make the equation easier. Binomial expansions can help them because, generally, if you expand and simplify the questions step by step, it is easy to see where your conclusion is going to and there will be a lower chance of error as you will see what you have done, step by step. Click to continue when do numbers become cumbersome ? Text Numbers become cumbersome when the number needing to be squared or multiplied by a power which is large and complex. Generally, a number gets harder when there are more than two decimals to multiply. An example of a really hard number is (169+1234)5= It can be very time consuming and cumbersome to multiply a binomial that is raised to the 6th, 20th, 30th power or higher. This is when long division may be slightly easier to use. Click to When is long multiplication more efficient more efficient then binomial expansion? It is easier to multiply single digit numbers. It is also easier to do long multiplication when multiplying tens, hundreds, thousands e.g. 100 x 100= 10000 or 1000 x 1000 = 1000000 etc. It is easy to do (10+10)2 long multiplication as you don’t need to go through “F.O.I.L.” Click to Bibliography Of course, the things we learnt in class. Oswego City School District Regents Exam Prep Center, Donna Roberts. "Binomial Theorem." Oswego City School District Regents Exam Prep Center. Web. 03 Nov. 2010. <http://www.regentsprep.org/Regents/math/algtrig/ATP4/bintheorem.htm>. "Statistics Tutorial: Binomial Distribution." Stat Trek: Teach Yourself Statistics. Web. 03 Nov. 2010. <http://stattrek.com/Lesson2/Binomial.aspx>. "Long Multiplication or Binomial Expansion? - Yahoo! Answers." Yahoo! Answers - Home. 31 Oct. 2010. Web. 03 Nov. 2010. <http://answers.yahoo.com/question/index?qid=20101030040321AABxvrn>