Factorize each of the following:27x^3+125z^2

(i) Using identity,

x³ + y³ = (x + y) (x² – xy + y²)

27y³ + 125z³ = (3y)³ + (5z)³

= (3y + 5z) {(3y)² – (3y) (5z) + (5z)²

= (3y + 5z) (9y² – 15yz + 25z)²

(ii) Using identity,

x³ – y³ = (x – y) (x² + xy + y²)

64m³ – 343n³ = (4m)³ – (7n)³

= (4m + 7n) {(4m)² + (4m) (7n) + (7n)²}

= (4m + 7n) (16m² + 28mn + 49n)²