Question

How do you factor `2p^3-162p`?

Answer 1

`2p(p-9)(p+9)`

Explanation:

The first step is to take out the `color(blue)"common factor"` of 2p

`rArr2p(p^2-81)tocolor(red)((1)`

`" the factor " (p^2-81)" is a " color(blue)"difference of squares"`

`"and 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=p" and " b=9`

`rArrp^2-81=(p-9)(p+9)`

`"returning to " color(red)((1))`

`rArr2p^3-162p=2p(p-9)(p+9)`