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Question
Using the identity (x + a)(x + b) = x2 + x(a + b) + ab, find the following product
(4x + 3y)(4x + 5y)
Solution
(4x + 3y)(4x + 5y)
Substituting x = 4x, a = 3y and b = 5y
In (x + a)(x + b) = x2 + x(a + b) + ab, we get
(4x + 3y)(4x + 5y) = (4x)2 + 4x(3y + 5y) + (3y)(5y)
= 42x2 + 4x(8y) + 15y2
= 16x2 + 32xy + 15y2
(4x + 3y)(4x + 5y) = 16x2 + 32xy + 15y2
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