Question: Factorize:
$4 x^{2}+9 y^{2}+16 z^{2}+12 x y-24 y z-16 x z$
Solution:
We have :
$4 x^{2}+9 y^{2}+16 z^{2}+12 x y-24 y z-16 x z$
$=(2 x)^{2}+(3 y)^{2}+(-4 z)^{2}+2(2 x)(3 y)+2(3 y)(-4 z)+2(-4 z)(2 x)$
$=[(2 x)+(3 y)+(-4 z)]^{2}$
$=(2 x+3 y-4 z)^{2}$
