1. ## Find the coeficient

Find the coefficient of the terms in x as indicated , in the following expansions .

(a) $(1+x)^2(2-3x)^7$ , term in x^3

(b) $(x+\frac{1}{x})^2(1-x)^5$ , term in x^2 .

Thanks .

2. In the expansion of $(a+b)^n$ the $(n+1)th$ term is given by

$
T_{n+1} = ~~ ^{n}C_r a^{n-r} b^{r}
$

(a)

, term in x^3

=(x^2+2x+1) (2-3x)^7

$
=\underbrace{x^2(2-3x)^7}_a +\underbrace{2x(2-3x)^7}_b +\underbrace{ 1(2-3x)^7}_c
$

For (a)
For getting x^3 the degree of x in second term should be one
(see the formula above)
Hence
in
$(2-3x)^7$

$
T_2 = ~~^7 C_1 2^{7-1} (-3x)^{1}
$

eliminate x to get value of coefficient
Go ahead with the b and c other terms

2)

(b) , term in x^2 .

If you understood 1 you can do it tell incase if you get stuck again