Binomial Expansion 4

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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

a)

$(\var{c4}+\var{c3}x)^{\var{c1}}$ $[x^{\var{c2}}]$

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b)

$(\var{d4}+\var{d3}x)^{\var{d1}}$ $[x^{\var{d2}}]$

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c)

$(\var{e4}-\var{e3}x)^{\var{e1}}$ $[x^{\var{e2}}]$

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d)

$(\var{f4}-\var{f3}x)^{\var{f1}}$ $[x^{\var{f2}}]$

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e)

$(\frac{1}{\var{g1}}+\frac{\var{g2}}{\var{g3}}x)^\var{g4}$ $[x^\var{g5}]$

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f)

$(\frac{1}{\var{h1}}-\frac{\var{h2}}{\var{h3}}x)^\var{h4}$ $[x^\var{h5}]$

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Advice

Recall the binomial theorem (a + b)^n = sum[k=0,n][(n over k)a^(n-k)b^k] and use this to answer each part

For example, if we want to know the coefficient of the $x^i$ term in $(a+bx)^n$ then we look at the binomial theorem and can see that the coefficient will be $\simplify{comb(n, i)}*a^{(n-i)}*b^i$

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Binomial Expansion 4

a)

b)

c)

d)

e)

f)

Advice