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Question

Resolve into factors:
4x4+25y4+10x2y2

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Solution

We know the identity a4+b4+a2b2=(a2+b2+ab)(a2+b2ab)

Using the above identity, the equation 4x4+25y4+10x2y2 can be factorised as follows:

4x4+25y4+10x2y2=(2x)4+(5y)4+(2x)2(5y)2
=[(2x)2+(5y)2+(2x)(5y)][(2x)2+(5y)2+(2x)(5y)]=(2x2+5y2+10xy) (2x2+5y210xy)

Hence, 4x4+25y4+10x2y2=(2x2+5y2+10xy)(2x2+5y210xy)


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