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Question
Factorise the following:
(a + b)2 + 9(a + b) + 18
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Solution
Let (a + b) = x
x2 + 9x + 18
Product = 18, sum = 9
Split the middle term as 6x and 3x
x2 + 9x + 18 = x2 + 6x + 3x + 18
= x(x + 6) + 3(x + 6)
= (x + 6)(x + 3)
But x = a + b
(a + b)2 + 9(a + b) + 18 = (a + b + 6)(a + b + 3)
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