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

Question

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

Accepted Answer

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

then $A=(1-3+10)^n=8^n$ (put $x=1$)
and sum of coefficients in the expansion of

$$\begin{aligned}
& \left(1+x^2\right)^n=B \
& \text { then } B=(1+1)^n=2^n \
& A=B^3
\end{aligned}$$

Solutions · 1