Question

How do you factor `36p^4-48p^3+16p^2`?

Answer 1

`4p^2*(3p-2)^2`
OR
`(6p^2-4p)^2`

Explanation:

Fist we factor out `p^2` leaving us with:
`p^2(36p^2-48p+16)`
We can also factor out `4` from all 3 terms so we get
`4p^2(9p^2-12p+4)`
Now, looking at `9p^2-12p+4` I see that `3p*3p=9p^2` and `(-2)*(-2)=4` and `(-2*3)+(-2*3)=-12`. That means that:
`9p^2-12p+4=(3p-2)(3p-2)=(3p-2)^2`

So final equation is `4p^2*(3p-2)^2`

Another answer is if we recognize that `4p^2=(2p)^2` and distribute `2p` into each of the `(3p-2)` leaving each term as `(6p^2-4p)` so the final answer would be:
`(6p^2-4p)^2`