Question

Resolve each of the following quadratic trinomials into factors:

(2a - b)² + 2(2a - b) - 8

Answer 1

Here, coefficient of (2a – b)² = 1, coefficient of (2a – b) = 2 and constant term = - 8

We shall now split up the coefficient of middle term i.e., 2 into two parts whose sum is 2 and product is -8 (1) = - 8

Clearly,

4 - 2 = 2 and

4 (-2) = - 8

So, we replace 2 (2a – b) = 4 (2a –b) – 2 (2a – b)

Thus, we have

(2a – b)² + 2 (2a – b) – 8 = (2a – b)² + 4 (2a – b) – 2 (2a – b) - 8

= (2a – b) (2a – b + 4) – 2 (2a – b + 4)

= (2a – b – 2) (2a – b + 4)