Question

Factorise fully x^3-x

Answer 1

`x(x+1)(x-1)`

Explanation:

We see that the two terms share an x, so we can pull that out:

`x^3-x=x(x^2-1)`

Now notice that we have a difference of squares (
`x^2-1`). Given a difference of squares,
`a^2-b^2`, this can always be factored into
`(a+b)(a-b)`. We can use this in this case:
`x^2-1=(x+1)(x-1)`.

So, our final factorized form is:
`x(x+1)(x-1)`.

Hope this helps!