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Question
Factorize x2 - y2 - 4xz + 4z2
Solution
On rearranging the terms
= x2 - 4xz + 4z2 - y2
= (x)2 - 2 x x 2z + (2z )2 - y2
Using identity a2 - 2ab + b2 = (a - b)2
= ( x - 2z )2 - y2
Using identity a2 - b2 = (a + b)(a - b)
= ( x - 2z + y )( x - 2z - y )
∴ x2 - y2 - 4xz + 4z2 = ( x - 2z + y )( x - 2z - y)
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