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Question #10746

1 Answer

A. S. Adikesavan

Dec 25, 2016

#-1024#

Explanation:

#(1+2x-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#

= the coefficient in the expansion of #((2-x)^2)^4)=(2-x)^8#

#=-8C_7 2^7=8 X 128=1024#, using binomial expansion

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