Question

Factorise fully x^3-x

Answer 1

Answer:

$x(x+1)(x-1)$

Step-by-step 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!