Factorize each of the following:

 i) 27y3+125z3

(ii) 64m3–343n3

Solutions:

(i) 27y3+125z3

The expression, 27y3+125z3 can be written as (3y)3+(5z)3

27y3+125z3 = (3y)3+(5z)3

We know that, 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) 64m3–343n3

The expression, 64m3–343n3can be written as (4m)3–(7n)3

64m3–343n3 =
(4m)3–(7n)3

We know that, 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+49n2)