Question

How do you factor `(3x-5)^3-125`?

Answer 1

`(3x-5)^3-125=(3x-10)(9x^2-15x+25)`

Explanation:

To factorize `(3x-5)^3-125`, as it is difference of two cubes, we can use the identity `a^3-b^3=(a+b)(a^2+ab+b^2)`. Hence,

`(3x-5)^3-125`

= `(3x-5-5)((3x-5)^2+5(3x-5)+5^2`

= `(3x-10)(9x^2-30x+25+15x-25+25)`

= `(3x-10)(9x^2-15x+25)`