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