Factorize:

Question:

Factorize: 

$9 x^{2}+16 y^{2}+4 z^{2}-24 x y+16 y z-12 x z$

 

Solution:

We have :

$9 x^{2}+16 y^{2}+4 z^{2}-24 x y+16 y z-12 x z$

$=(-3 x)^{2}+(4 y)^{2}+(2 z)^{2}+2(-3 x)(4 y)+2(4 y)(2 z)+2(2 z)(-3 x)$

$=[(-3 x)+(4 y)+(2 z)]^{2}$

$=(-3 x+4 y+2 z)^{2}$

 

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