Question 21702
{{{x^3 - 36x}}} really means x*x*x - 36*x. So, what appears in both terms? An x does. So take this out of both terms...ie factorise, leaving x*(x*x - 36), which is written as {{{x(x^2 - 36)}}}.


This is your answer.


However, {{{x(x^2 - 36)}}} can be thought of as {{{x(x^2 - 6^2)}}}. Being able to write terms within the bracket as the "difference of squares" means we can write this is a factored pair, as follows:


{{{x(x-6)(x+6)}}}


This is now fully factored... multiply out the brackets to make you fully accept that it is in fact {{{x^2-36}}}


jon.