How do you factor #5u^3-40(x+y)^3#?
1 Answer
May 15, 2016
#5u^3-40(x+y)^3=5(u-2x-2y)(u^2+2ux+2uy+4x^2+8xy+4y^2)#
Explanation:
We will use the difference of cubes identity:
#a^3-b^3 = (a-b)(a^2+ab+b^2)#
with
First separate out the common scalar factor
#5u^3-40(x+y)^3#
#=5(u^3-8(x+y)^3)#
#=5(u^3-(2(x+y))^3)#
#=5(u-2(x+y))(u^2+u(2(x+y))+(2(x+y))^2)#
#=5(u-2x-2y)(u^2+2ux+2uy+4x^2+8xy+4y^2)#
