Question

How do you factor `3r^3-192r`?

Answer 1

`3r(r-8)(r+8)`

Explanation:

The first step is to take out a `color(blue)"common factor"` of 3r

`rArr3r(r^2-64)`

We now have a `color(blue)"difference of squares"` inside the bracket, which factorises in general as.

`color(red)(bar(ul(|color(white)(2/2)color(black)(a^2-b^2=(a-b)(a+b))color(white)(2/2)|)))`

`"here " a = r" and " b=8`

`rArrr^2-64=(r-8)(r+8)`

`"Pulling it all together gives"`

`3r^3-192r=3r(r-8)(r+8)`