CF Maths January test mock paper Binomial Expansion 6

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Question 1

Find the coefficient of the term indicated in the square brackets in the expansion of each of the following expressions below

$(\var{c3}-x)(1+x)^{\var{c1}}$ $[x^{\var{c2}}]$

Expected answer:

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Advice

In these questions we need to think carefully about which terms in the expansions will contribute to the coefficient that we are trying to find.

For example, if we have $(a+bx)(c+dx)^n$ and we are looking for the coefficient of the $x^i$ term then the answer will be $a*\simplify{comb(n,i)}*d^i + b*\simplify{comb(n, i-1)}*d^{i-1}$

This makes use of the binomial theorem:

(a + b)^n = sum[k=0,n][(n over k)a^(n-k)b^k]

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CF Maths January test mock paper Binomial Expansion 6

Advice