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Question

Expand the following polynomial
(xy3)2+(x2y+xy2)2+(x+y)2

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Solution

(xy3)2+(x2y+xy2)2+(x+y)2=13(x22xy+y2)+(x4y2+2x3y3+x2y4)+(x2+2xy+y2)
=x4y2+2x3y3+x2y4+43x2+43xy+43y2

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