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 - 9)(y + 2).

Hence, y² - 7y - 18 = (y - 9)(y + 2).