Factorize each of the following:

[Hint: See Question 9]

(i) 27y3 + 125z3

(ii) 64m3 – 343n3

(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 + 25z2)


(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

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