How do you factor #x^3+x^2-125p^3-25p^2#?

1 Answer
Sep 23, 2016

Answer:

#x^3+x^2-125p^3-25p^2 = (x-5p)(x^2+5px+25p^2+x+5p)#

Explanation:

The difference of squares identity can be written:

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

The difference of cubes identity can be written:

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

So we find:

#x^3+x^2-125p^3-25p^2 = (x^3-(5p)^3)+(x^2-(5p)^2)#

#color(white)(x^3+x^2-125p^3-25p^2) = (x-5p)(x^2+5px+25p^2)+(x-5p)(x+5p)#

#color(white)(x^3+x^2-125p^3-25p^2) = (x-5p)(x^2+5px+25p^2+x+5p)#

This has no simpler factors.