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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Question Number 63941 by gunawan last updated on 11/Jul/19

$If the sum of the coefficients in the expansion$ $of {(1 - 3 x + 10 x^{2})}^{n} is a and if the sum of the$ $coefficients in the expansion of {(1 + x^{2})}^{n} is$ $b, then$
	Answered by mr W last updated on 11/Jul/19

	${(1 - 3 x + 10 x^{2})}^{n} = Σ A_{r} x^{r}$ $l e t x = 1 :$ ${(1 - 3 + 10)}^{n} = Σ A_{r} = a$ $\Rightarrow a = 8^{n} = 2^{3 n} = {(2^{n})}^{3}$ ${(1 + x^{2})}^{n} = Σ B_{r} x^{r}$ $l e t x = 1 :$ ${(1 + 1)}^{n} = Σ B_{r} = b$ $\Rightarrow b = 2^{n}$ $\Rightarrow a = b^{3}$
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