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(B) To find the sum of the coefficients in the expansion of a polynomial $P(x)$,we substitute $x = 1$.For the expansion $(1 - 3x + 10x^2)^n$,the sum o

Vedclass · Accepted Answer

$a = b^3$

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(B) To find the sum of the coefficients in the expansion of a polynomial $P(x)$,we substitute $x = 1$.For the expansion $(1 - 3x + 10x^2)^n$,the sum of the coefficients $a$ is given by:$a = (1 - 3(1) + 10(1)^2)^n = (1 - 3 + 10)^n = 8^n = (2^3)^n = 2^{3n}$.For the expansion $(1 + x^2)^n$,the sum of the coefficients $b$ is given by:$b = (1 + (1)^2)^n = (1 + 1)^n = 2^n$.Comparing $a$ and $b$,we have $a = (2^n)^3 = b^3$.Thus,$a = b^3$.

If the sum of the coefficients in the expansion of $(1 - 3x + 10x^2)^n$ is $a$ and if the sum of the coefficients in the expansion of $(1 + x^2)^n$ is $b$,then:

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