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Factorisation by Common Factors

Factorise:13 ...

Question

Factorise:

(13) 16m² – 40mn + 25n²

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Solution

16m² – 40mn + 25n²
= (4m)² – 2 × 4m × 5n + (5n)²
= (4m – 5n)² [a² – 2ab + b² = (a – b)²]
= (4m – 5n) (4m – 5n)
∴ 16m² – 40mn + 25n² = (4m – 5n) (4m – 5n)

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