Factorize:

Question:

Factorize: 

$25 x^{2}+4 y^{2}+9 z^{2}-20 x y-12 y z+30 x z$

 

Solution:

We have :

$25 x^{2}+4 y^{2}+9 z^{2}-20 x y-12 y z+30 x z$

$=(5 x)^{2}+(-2 y)^{2}+(3 z)^{2}+2(5 x)(-2 y)+2(-2 y)(3 z)+2(3 z)(5 x)$

$=[(5 x)+(-2 y)+(3 z)]^{2}$

$=(5 x-2 y+3 z)^{2}$

 

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