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

1 Answer
Oct 20, 2015

Answer:

#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)#