Find the coefficient of the terms in x as indicated , in the following expansions .
(a) $\displaystyle (1+x)^2(2-3x)^7$ , term in x^3
(b) $\displaystyle (x+\frac{1}{x})^2(1-x)^5$ , term in x^2 .
Thanks .
In the expansion of $\displaystyle (a+b)^n$ the $\displaystyle (n+1)th $ term is given by
$\displaystyle
T_{n+1} = ~~ ^{n}C_r a^{n-r} b^{r}
$
(a)
, term in x^3
=(x^2+2x+1) (2-3x)^7
$\displaystyle
=\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
$\displaystyle (2-3x)^7 $
$\displaystyle
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