Question

Factorise the question 9x^2-6xy+y^2-z^2
Make sure the answer is (3x-y+z)(3x-y-z)​

Answer 1

9x² - 6xy + y² - z²

= (9x² - 6xy + y²) - z²

= {(3x)² - 2(3x)(y) + (y)²} - z²

We know that x² - 2xy + y² = (x - y)²

Here x = 3x, y = y

By substituting the values :

= (3x - y)² - z²

Here, Consider x = 3x - y, y = z

We know that, x² + y² = (x + y)(x - y)

By substituting the values :

= (3x - y + z)(3x - y - z)

Hope it helps!