If A denotes the sum of all the coefficients in the expansion of (1-3x+10x^2)^n and B deno…

Question

If A denotes the sum of all the coefficients in the expansion of ${(1-3x+10{x}^{2})}^{n}$ and B denotes the sum of all the coefficients in the expansion of ${(1+{x}^{2})}^{n}$, then :

Accepted Answer

Sum of coefficients in the expansion of ${(1-3x+10{x}^{2})}^{n}=A$

then $A=(1-3+10{)}^{n}={8}^{n}$ (put $x=1$)<?p>
and sum of coefficients in the expansion of

$\begin{gathered} {(1+{x}^{2})}^{n}=B \ B=(1+1{)}^{n}={2}^{n} \ A={B}^{3} \end{gathered}$

Solutions · 1