Factorize the following expression:
4(xy+1)2−9(x−1)2
Given expression: 4(xy+1)2−9(x−1)2
=(2)2(xy+1)2−(3)2(x−1)2
=[2(xy+1)]2−[3(x−1)]2
=(2xy+2)2−(3x−3)2
Since, we have the formula
(a2−b2)=(a+b)(a−b)
On Substituting a=(2xy+2),b=(3x−3) in above formula
⇒(2xy+2)2−(3x−3)2=(2xy+2+3x−3)(2xy+2−3x+3)
⇒(2xy+2)2−(3x−3)2=(2xy+3x−1)(2xy−3x+5)
∴4(xy+1)2−9(x−1)2=(2xy+3x−1)(2xy−3x+5)