Question

Using the identity (x + a)(x + b) = x² + x(a + b) + ab, find the following product

(8 + pq)(pq + 7)

Answer 1

(8 + pq)(pq + 7)

Substituting x = pq, a = 8 and b = 7

In (x + a)(x + b) = x² + x(a + b) + ab, we get

(pq + 8)(pq + 7) = (pq)² + pq(8 + 7) + (8)(7)

= p²q² + pq(15) + 56

(8 + pq)(pq + 7) = p²q² + 15pq + 56