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Question #10746

1 Answer

A. S. Adikesavan

Dec 25, 2016

$- 1024$ $-1024$

Explanation:

${(1 + 2 x - x^{2})}^{4}$ $(1+2x-x^2)^4$

$= {(2 - {(1 - x)}^{2})}^{4}$ $=(2-(1-x)^2)^4$

= terms that do not contribute to the coefficient of #x^7

the last term ((2-x)^2)^4#, using binomial expansion

So, the coefficient of $x^{7}$ $x^7$

= the coefficient in the expansion of ${({(2 - x)}^{2})}^{4}) = {(2 - x)}^{8}$ $((2-x)^2)^4)=(2-x)^8$

$= - 8 C_{7} 2^{7} = 8 X 128 = 1024$ $=-8C_7 2^7=8 X 128=1024$ , using binomial expansion

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