Factor completely a^2-ab-12 b^2

In order to factor this, you need to look at the coefficient of the last term which is - 12. After that, you need to think of two factors of this number that would yield to - 1 (which is the coefficient of the second term) when added or subtracted. You will get - 4 and 3 (-4 + 3 = - 1). Therefore, the expression would become (a - 4b) (a + 3b). This expression is the complete factors of the expression given.

Note: This is applicable when the coefficient of the first term is 1.