Question

Factorize:

(x + 2)3 + (x − 2)3

Answer 1

(x+2)3 + (x−2)3 [p3 + q3 = (p + q)(p2 – pq + q2)]

Here p = x + 2 and q = x – 2

= (x + 2 + x − 2)((x + 2)2−(x + 2)(x − 2) + (x − 2) 2)

= 2x(x2 + 4x + 4 − (x + 2)(x − 2) + x2 − 4x + 4) [(a + b)(a − b) = a2 − b2]

= 2x(2x2 + 8 − (x2 − 22))

= 2x(2x2 + 8 − x2 + 4)

= 2x(x2 + 12)