Question: Factorize:
$25 x^{2}+4 y^{2}+9 z^{2}-20 x y-12 y z+30 x z$
Solution:
We have :
$25 x^{2}+4 y^{2}+9 z^{2}-20 x y-12 y z+30 x z$
$=(5 x)^{2}+(-2 y)^{2}+(3 z)^{2}+2(5 x)(-2 y)+2(-2 y)(3 z)+2(3 z)(5 x)$
$=[(5 x)+(-2 y)+(3 z)]^{2}$
$=(5 x-2 y+3 z)^{2}$
