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Question

Factorize:

4(xy)2+12(xy)(x+y)+9(x+y)2

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Solution

4(xy)2+12(xy)(x+y)+9(x+y)2

=[2(xy)]2+2×2(xy)×3(x+y)+[3(x+y)]2

[Using the identity,a2+2×a×b+b2=(a+b)2]

Here, a=2(xy), b=3(x+y)

=[2(xy)+3(x+y)]2

=(2x2y+3x+3y)2

=(5x+y)2


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