How do you factor #27x^3-125#?

1 Answer
Dec 11, 2015

Answer:

#= (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 =)