How do you factor 27x^3-125?

1 Answer
Dec 11, 2015

= (3x-5) (9x^"2" +15x+25)

Explanation:

you can remember to factor difference between 2 cubes as this

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

so the answer to your question..

27x^"3"−125 can be written as
=3^"3"x^"3" - 5^"3"
= (3x-5) (9x^"2" +15x+25)

FYI: an addition between 2 cubes can be written as this
a^"3" + b^"3" = (a+b) (a^2 - ab + b^2)
it's really easy when you remember those two equations by their patterns =)