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Factors of Algebraic Expressions and Factorisation

Factorise:16 ...

Question

Factorise:

(16) 64 – 48n + 9n²

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Solution

64 – 48n + 9n²
= (8)² – 2 × 8 × 3n + (3n)²
= (8 – 3n)² [a² – 2ab + b² = (a – b)²]
= (8 – 3n) (8 – 3n)
∴ 64 – 48n + 9n² = (8 – 3n) (8 – 3n)

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