Factorise the following:

1 - 18y - 63y²

To factorise 1 - 18y - 63y², we want to find two real numbers whose sum is -18 and product is 1 × (-63) = -63. By trial, we see that -21 + 3 = -18 and -21 × 3 = -63.

∴ 1 - 18y - 63y² = 1 - 21y + 3y - 63y²

= 1(1 - 21y) + 3y(1 - 21y)

= (1 - 21y)(1 + 3y).

Hence, 1 - 18y - 63y² = (1 - 21y)(1 + 3y).