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Question

Factorise:

(7) 25m2 + 90mn + 81n2

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Solution

25m2 + 90mn + 81n2
= (5m)2 + 2 × 5m × 9n + (9n)2
= (5m + 9n)2 [a2 + 2ab + b2 = (a + b)2]
= (5m + 9n) (5m + 9n)
∴ 25m2 + 90mn + 81n2 = (5m + 9n) (5m + 9n)

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