How do you factor #8x^3 - (2x - y)^3#?

1 Answer
Jun 28, 2018

Answer:

#y(12x^2-6xy+y^2)#

Explanation:

#"this is a "color(blue)"difference of cubes"#

#"which factors in general as"#

#•color(white)(x)a^3-b^3=(a-b)(a^2+ab+b^2)#

#8x^3=(2x)^3rArra=2x" and "b=2x-y#

#=(2x-(2x-y))((2x)^2+2x(2x-y)+(2x-y)^2)#

#=y(4x^2+4x^2-2xy+4x^2-4xy+y^2)#

#=y(12x^2-6xy+y^2)#