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Summary OCR MEI Mathematics: Year 1 (AS) Pure - Binomial Expansion Cheat Sheet $3.86
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Summary OCR MEI Mathematics: Year 1 (AS) Pure - Binomial Expansion Cheat Sheet

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This document briefly summarises the 'Binomial Expansion' topic of the Year 1 (AS) Pure section of the OCR MEI Mathematics A Level Course.

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  • January 22, 2021
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  • 2020/2021
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By: tsmith3553 • 1 year ago

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Binomial Expansion
Pascal’s Triangle




Courtesy of Wikipedia
● You can expand an expression in the form (a + b)n using Pascal’s triangle
● Find the n th row of the triangle
● The coefficient of each term is multiplied by the corresponding number on
the row of the triangle (ie the second term’s coefficient is multiplied by the
second number in the appropriate row of the triangle)
● The first term is an and the powers of a decrease by 1 each term (so the
final term has no a in it)
● The first term has no b in it and the powers of b increase by 1 each term (so
the final term is bn


Combinations
● For large values of n , using Pascal’s triangle is impractical
● Instead use ​n​C​r to
​ give the coefficient multiplication numbers
n!
r!(n−r)!
● n is the power to which the entire bracket is raised, r is the power to which
the x of the desired term is raised
● n​C​r​ is the same as saying “How many ways are there of taking r items from
a collection of n items”
● P​ is called Permutations and is the same except is used when order
n​ r​
matters (ie if different orders are different unique entities) and so will give a
higher number than ​n​C​r


Approximations
● Can be used to make approximations of decimals raised to certain powers
● For example 1.02​30​ is the same as (1 + 2x)30 where x is equal to 0.01
● Therefore to approximate, use binomial expansion to find the first three or
four terms and substitute x = 0.01

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