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Question:

Factorise each of the following: (i) 27y³ + 125z³ (ii) 64m³ - 343n³

Solution:

(i) 27y³ + 125z³ = (3y)³ + (5z)³ = (3y + 5z)(3y)² - (3y)(5z) + (5z)² = (3y + 5z)(9y² - 15yz + 25z²)
(ii) 64m³ - 343n³ = (4m)³ - (7n)³ = (4m - 7n)(4m)² + (4m)(7n) + (7n)² = (4m - 7n)(16m² + 28mn + 49n²)