Question
Factorise:
$9 x^2+16 y^2+4 z^2-24 x y+16 y z-12 x z$
$9 x^2+16 y^2+4 z^2-24 x y+16 y z-12 x z$
✓
Answer
We have:
$9 x^2+16 y^2+4 z^2-24 x y+16 y z-12 x z$
$=(2 x)^2+(3 y)^2+(-4 z)^2+2(2 x)(3 y)+2(3 y)(-4 z)+2(-4 z)(2 x)$
$=[(2 x)+(3 y)+(-4 z)]^2$
$=(2 x+3 y-4 z)^2$
$9 x^2+16 y^2+4 z^2-24 x y+16 y z-12 x z$
$=(2 x)^2+(3 y)^2+(-4 z)^2+2(2 x)(3 y)+2(3 y)(-4 z)+2(-4 z)(2 x)$
$=[(2 x)+(3 y)+(-4 z)]^2$
$=(2 x+3 y-4 z)^2$
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