Question
Factorise:
4x2 + 9y2 + 16z2 + 12xy - 24yz - 16xz
4x2 + 9y2 + 16z2 + 12xy - 24yz - 16xz
✓
Answer
We have:
4x2 + 9y2 + 16z2 + 12xy - 24yz - 16xz
= (2x)2 + (3y)2 + (-4z)2 + 2(2x)(3y) + 2(3y)(-4z) + 2(-4z)(2x)
= [(2x) + (3y) + (-4z)]2
= (2x + 3y - 4z)2
4x2 + 9y2 + 16z2 + 12xy - 24yz - 16xz
= (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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