If a and b denote the sum of the coefficients in the expansions of

Question:

If $a$ and $b$ denote the sum of the coefficients in the expansions of $\left(1-3 x+10 x^{2}\right)^{n}$ and $\left(1+x^{2}\right)^{n}$ respectively, then write the relation between $a$ and $b$.

Solution:

Here,

$a=1-3+10=8=2^{3}$

$b=1+1=2$

$\Rightarrow a=b^{3}$