Question

64x cube +root 125y cube factorize

Answer 1

Answer:

given 64 x^3 + 125 y^3

as both terms are perfect cube, we can use the identity a^3 + b^3 = (a+b)(a^2-ab+b^2)

we can rewrite the given expression as

(4 x)^3 + (5 y)^3

on comparing, a = 4x and b = 5y

=> now we can factorise the expression as

(4x+5y)[ (4x)^2 - 4x×5y + (5y)^2 ]

=> (4x+5y)(16x^2 - 20 xy + 25y^2)