Question
Factorise:
16x2 + 4y2 + 9z2 - 16xy - 12yz + 24xz
16x2 + 4y2 + 9z2 - 16xy - 12yz + 24xz
✓
Answer
We have:
16x2 + 4y2 + 9z2 - 16xy - 12yz + 24xz
= (4x)2 + (-2y)2 + (3z)2 + 2(4x)(-2y) + 2(-2y)(3z) + 2(3z)(4x)
= (4x - 2y + 3z)2 [using a2 + b2 + c2 + 2ab + 2bc + 2ca = (a + b + c)2]
Hence, 16x2 + 4y2 + 9z2 - 16xy - 12yz + 24xz = (4x - 2y + 3z)2
16x2 + 4y2 + 9z2 - 16xy - 12yz + 24xz
= (4x)2 + (-2y)2 + (3z)2 + 2(4x)(-2y) + 2(-2y)(3z) + 2(3z)(4x)
= (4x - 2y + 3z)2 [using a2 + b2 + c2 + 2ab + 2bc + 2ca = (a + b + c)2]
Hence, 16x2 + 4y2 + 9z2 - 16xy - 12yz + 24xz = (4x - 2y + 3z)2
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