How do you factor 8x³ + 125y³?

1 Answer
May 12, 2018

(2x+5y)(2x-5y)^2

Explanation:

8x^3 + 125y^3 is (2x)^3+(5y)^3

the sum of two cubes formula
a^3 + b^3 = (a+b)(a^2-ab+b^2)

so

(2x)^3+(5y)^3

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

now you can factor the second parentheses pair
(2x+5y)color(red)((4x^2-10xy+25y^2))

color(red)((4x^2-10xy+25y^2) = (2x-5y)^2)

(2x+5y)(2x-5y)^2