Transcript Math reflection on Binomial Expansions

Binomial Expansions
Reflection
By: Arsalaan Muhammad
Math: Mrs. Taher
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rule for expanding
binomials
These are 2 generalized expressions:
(a+b)2 = a2 + 2ab + b2
and:
(a-b)2 = a2 -2ab + b2
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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
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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.
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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.
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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.
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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.
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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.”
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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>