Question

Factorize:
x²-y²-4xz+4z²

Answer 1

Answer:

Please see the attachment

Answer 2

The expression is given as : x² – y² - 4xz + 4z²

Firstly we regroup the terms :

= x² – 4xz + 4z² – y²

= (x)² - 2 × x × 2z + (2z)²  – (y)²

By using an identity, a² - 2ab + b² = (a + b)² :  

= (x - 2z)² – y²

By using an identity, a² -  b² = (a + b) (a - b) :

= (x - 2z +  y) (x – 2z - y)

= (x – y – 2z) (x + y – 2z)

Hence,  the factorisation of x² – y² - 4xz + 4z²  is (x – y – 2z) (x + y – 2z).

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