Question

How do you factor `3x^2 y^2 -12xyz^2 +12z^4`?

Answer 1

`3(xy-2z^2)^2`

Explanation:

Temporarily replace
`color(white)("XXX")xy` with `a` and
`color(white)("XXX")z^2` with `b`
so we have
`color(white)("XXX")3a^2-12ab+12b^2`

which factors as
`color(white)("XXX")=3(a^2-4ab+4b^2`

`color(white)("XXX")=3(a-2b)^2`

Restoring the values for `a` and `b`
`color(white)("XXX")=3(xy-2z^2)`