Factorise the following:

x(x + z) - y(y + z)

x(x + z) - y(y + z) = x² + xz - y² - yz.

Rearranging the above terms we get,

x² - y² + xz - yz

We know that,

a² - b² = (a + b)(a - b).

∴ x² - y² + xz - yz = (x + y)(x - y) + z(x - y)

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

Hence, x(x + z) - y(y + z) = (x - y)(x + y + z).