Question
Factorise:
25x2 + 4y2 + 9z2 - 20xy - 12yz + 30xz.
25x2 + 4y2 + 9z2 - 20xy - 12yz + 30xz.
✓
Answer
We have:
25x2 + 4y2 + 9z2 - 20xy - 12yz + 30xz
= (5x)2 + (-2y)2 + (3z)2 + 2(5x)(-2y) + 2(-2y)(3z) + 2(3z)(5x)
= [(5x) + (-2y) + (3z)]2
= (5x - 2y + 3z)2
25x2 + 4y2 + 9z2 - 20xy - 12yz + 30xz
= (5x)2 + (-2y)2 + (3z)2 + 2(5x)(-2y) + 2(-2y)(3z) + 2(3z)(5x)
= [(5x) + (-2y) + (3z)]2
= (5x - 2y + 3z)2
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