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

Accepted Answer

Sum of all coefficients is obtained by putting $x=1$.

$A=(1-3+10)^n=8^n$

$B=(1+1)^n=2^n$

So $A=8^n=(2^n)^3=B^3$.

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