How do you factor 125a^3-c^3?

1 Answer
Jan 11, 2016

125a^3-c^3=(5a-c)*(25a^2+5ac+c^2)

Explanation:

125a^3-c^3=5^3a^3-c^3=(5a)^3-c^3

Using the difference of two cubes rule:

(b^3-d^3)=(b-d)(b^2+bd+d^2)

with:

b=5a
d=c

125a^3-c^3=(5a-c)(5^2a^2+5ac+c^2)=
=(5a-c)*(25a^2+5ac+c^2)