(A) The sum of all coefficients in the expansion of a polynomial $P(x)$ is obtained by substituting $x=1$ into the expression.For $A$,the sum of coeff

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(A) The sum of all coefficients in the expansion of a polynomial $P(x)$ is obtained by substituting $x=1$ into the expression.For $A$,the sum of coefficients in $(1-3x+10x^2)^n$ is:$A = (1-3(1)+10(1)^2)^n = (1-3+10)^n = 8^n$.For $B$,the sum of coefficients in $(1+x^2)^n$ is:$B = (1+(1)^2)^n = (1+1)^n = 2^n$.Now,express $A$ in terms of $B$:$A = 8^n = (2^3)^n = (2^n)^3$.Since $B = 2^n$,we have:$A = B^3$.

Class 11 Mathematics Binomial Theorem Expansion of binomial theorem

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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:

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A
$A=B^3$
B
$3A=B$
C
$B=A^3$
D
$A=3B$

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