Core 2 - Binomial Expansion Key points

Core 2 binomial expansion key points 

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Binomial Expansion ­ Key Points
(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
start at a power of bracket powers of a decrease
powers of b increase
power of a + power of b = power of bracket
The coefficients come from:
Pascal's Triangle or Calculator
(low powers)
1 1
1 2 1
1 3 3 1
1 4 6 4 1 e.g.
Include brackets
= 8x3 ­ 36 x2 + 54x ­ 27
a = 2x b = ­ 3
Pair of brackets
(2 ­ 5x) (1 + 2x)3 find the coefficient of x2
expand the second bracket as far as x2 using Binomial expansion
(2 ­ 5x) ( 1 + 3(2x) + 3(2x)2 ........
(2 ­ 5x) (1 + 6x + 12x2 ........
multiply the brackets together by finding pairs that give x2
= 24x2 ­ 30x2 = 6x2
Fractions

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