Resolve each of the following quadratic trinomials into factors:

Here, coefficient of a² = 36, coefficient of a = 12bc and constant term = - 15b²c²

We shall now split up the coefficient of middle term i.e., 12bc into two parts whose sum is 12bc and product is 36 (-15b²c²) = - 500b²c²

So, we replace middle term 12abc = 30abc – 18abc

Thus, we have

36a² –12abc– 15b²c² = 36a² + 30abc – 18abc – 15b²c²

= (6a + 5bc) (6a – 3bc)