Question

Factorise the following:
4xy - x² - 4y² + z²

Answer 1

4xy - x² - 4y² + z²
= z² - x² - 4y² + 4xy
= z² - (x² + 4y² - 4xy)
= z² - (x - 2y)²
= [z - (x - 2y)][z + (x - 2y)]
= (z - x + 2y)(z + x - 2y).