Factorise the following:

y² + 7y - 18

To factorise y² + 7y - 18, we want to find two real numbers whose sum is 7 and product is -18. By trial, we see that 9 + (-2) = 7 and 9 × -2 = -18.

∴ y² + 7y - 18 = y² + 9y + (-2y) - 18

= y² + 9y - 2y - 18

= y(y + 9) - 2(y + 9)

= (y - 2)(y + 9).

Hence, y² + 7y - 18 = (y - 2)(y + 9).