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Question

Factorise:

(9) 4b2 + 12ab + 9a2

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Solution

4b2 + 12ab + 9a2
= (2b)2 + 2 × 2b × 3a + (3a)2
= (2b + 3a)2 [a2 + 2ab + b2 = (a + b)2]
= (2b + 3a) (2b + 3a)
∴ 4b2 + 12ab + 9a2 = (2b + 3a) (2b + 3a)

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