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Question
Using the identity (x + a)(x + b) = x2 + x(a + b) + ab, find the following product
(8 + pq)(pq + 7)
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Solution
(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
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