Question

Factorize x² - y² - 4xz + 4z²

Answer 1

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)