How do you factor #8y^3-125#?

1 Answer
Feb 27, 2017

Answer:

#8y^3 - 125 = (2y-5)(4y^2+10y+25)#

Explanation:

The difference of cubes identity can be written:

#a^3-b^3 = (a-b)(a^2+ab+b^2)#

Use this with #a=2y# and #b=5# as follows:

#8y^3 - 125 = (2y)^3-5^3#

#color(white)(8y^3 - 125) = (2y-5)((2y)^2+(2y)(5)+5^2)#

#color(white)(8y^3 - 125) = (2y-5)(4y^2+10y+25)#