Question
Factorise :$4 x^2+9 y^2+16 z^2+12 x y-24 y z-16 x z$
✓
Answer
$4 x^2+9 y^2+16 z^2+12 x y-24 y z-16 x z$
$=(2 x)^2+(3 y)^2+(-4 z)^2+2(2 x)(3 y)$
$+2(3 y)(-4 z)+2(-4 z)(2 x)$
$=\{2 x+3 y+(-4 z)\}^2=(2 x+3 y-4 z)^2$
$=(2 x+3 y-4 z)(2 x+3 y-4 z)$
$=(2 x)^2+(3 y)^2+(-4 z)^2+2(2 x)(3 y)$
$+2(3 y)(-4 z)+2(-4 z)(2 x)$
$=\{2 x+3 y+(-4 z)\}^2=(2 x+3 y-4 z)^2$
$=(2 x+3 y-4 z)(2 x+3 y-4 z)$
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