Question

Coefficient of $x^4$ in the following expansion ${(2-\frac{3x^2}{2})}^4$ is

Answer 1

By binomial expansion

$(a+b{)}^n=\sum _{r=0}^n{}^n{C}_r{a}^{n-r}{b}^r$

Here, $a=2,n=4\&b=-\frac{3x^2}{2}$

$\therefore {(2-\frac{3x^2}{2})}^4=\sum _{r=0}^4{}^4{C}_r{2}^{4-r}{(-\frac{3x^2}{2})}^r$

On simplifying the bracket, we get the answer

${(2-\frac{3x^2}{2})}^4=16-48x^2+54x^4-27x^6+\frac{81x^8}{16}$