Factorise the following:

6x² - 5xy - 6y²

To factorise 6x² - 5xy - 6y², we want to find two real numbers whose sum is -5 and product is 6 × (-6) = -36. By trial, we see that -9 + 4 = -5 and (-9) × 4 = -36.

∴ 6x² - 5xy - 6y² = 6x² - 9xy + 4xy - 6y²

= 3x(2x - 3y) + 2y(2x - 3y)

= (2x - 3y)(3x + 2y).

Hence, 6x² - 5xy - 6y² = (2x - 3y)(3x + 2y).