# Core 2 - Binomial Expansion Key points

Core 2 binomial expansion key points

- Created by: Mahek Jazmin
- Created on: 13-08-11 18:08

First 122 words of the document:

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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