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