Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

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

1 Answer

Oct 20, 2015

$3 {(x y - 2 z^{2})}^{2}$ $3(xy-2z^2)^2$

Explanation:

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

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

$XXX = 3 {(a - 2 b)}^{2}$ $color(white)("XXX")=3(a-2b)^2$

Restoring the values for $a$ $a$ and $b$ $b$
$XXX = 3 (x y - 2 z^{2})$ $color(white)("XXX")=3(xy-2z^2)$

Related questions

See all questions in Factoring Completely

Impact of this question

1388 views around the world

You can reuse this answer
Creative Commons License