Question

Coefficient of $x^6$ in the following expansion ${(3a-\frac{2}{3})}^6$ is

Answer 1

Using binomial equation we know that

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

In the given question $p=3a,n=6\&q=-\frac{2}{3}$

$\therefore {(3a-\frac{2}{3})}^6=\sum _{r=0}^n{}^6{C}_r{3a}^{6-r}{l(-\frac{2}{3})}^r$

On simplifying, we get

${(3a-\frac{2}{3})}^6=\frac{16}{81}-\frac{32a}{9}+24a^2-72a^3+81a^4$