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Binomial Expansion

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Prerequist Materials:

Pascal's Triangle

Permutations and Combinations

Expanding Brackets:

(a+b)0=1 (a+b)1=a+b (a+b)2 =a2+2ab+b2 (a+b)3 =a3 +3a2b +3ab2 +b3 (a+b)4 =a4 +4a3b +6a2b2 +4ab3 +b4

From these expansions we can see that the coefficients of each term are the elements of Pascal's Triangle, and the powers of a count down to one from left to right, whereas, the powers of b count up from one. So...

(a+b)n = (n0) an + (n1) an-1 b + (n2) an-2 b2 + + (nn-2) a2 bn-2 + (nn-1) a bn-1 + (nn) bn


binomial expansion

(1+x)n =1+nx +n(n-1)x22! +n(n-1)(n-2)x33! +...

where n.

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