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Question

Factorize the following expression:
4(xy+1)29(x1)2

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Solution

Given expression: 4(xy+1)29(x1)2

=(2)2(xy+1)2(3)2(x1)2

=[2(xy+1)]2[3(x1)]2

=(2xy+2)2(3x3)2

Since, we have the formula

(a2b2)=(a+b)(ab)

On Substituting a=(2xy+2),b=(3x3) in above formula

(2xy+2)2(3x3)2=(2xy+2+3x3)(2xy+23x+3)

(2xy+2)2(3x3)2=(2xy+3x1)(2xy3x+5)

4(xy+1)29(x1)2=(2xy+3x1)(2xy3x+5)


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