Q.10. Factorise each of the following:

(i) 27y3 + 125z3 (ii) 64m3 - 343n3

Solution:

(i) Using identity, x3 + y3 = (x + y) (x2 - xy + y2)

We have, 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 )

We have, 64m3 - 343n3 = (4m)3 - (7n)3

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

= (4m + 7n) (16m2 + 28mn + 49n2)