How do you factor #32x^3-500y^3#?

1 Answer
Dec 30, 2015

Answer:

#4(2x - 5y)(4x^2 + 10xy + 25y^2)#

Explanation:

First extract common factors
#(32x^3 - 500 y^3) = 4(8x^3 - 125y^3)#
The term in brackets is now the difference of cubes, which can be factored as #a^3 – b^3 = (a – b)(a^2 + ab + b^2)#
So
#32x^3 - 500y^3 = 4(2x - 5y)(4x^2 + 10xy + 25y^2)#