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Question

Simplify x4+2x3y2xy3y4

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Solution

We have,

x4+2x3y2xy3y4

=x4y4+2x3y2xy3

=(x2)2(y2)2+2xy(x2y2)

=(x2y2)(x2+y2)+2xy(x2y2)

=(x2y2)(x2+y2+2xy)

=(x2y2)(x+y)2

=(x+y)(xy)(x+y)2

=(x+y)3(xy)

Hence, this is the answer.

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