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Question
Factorise:
27x3 + y3 + z3 – 9xyz
Solution
It is known that,
x3 + y3 + z3 − 3xyz = (x + y + z) (x2 + y2 + z2 − xy − yz − zx)
∴ 27x3 + y3 + z3 – 9xyz = (3x)3 + (y)3 + (z)3 – 3(3x)(y)(z)
= (3x + y + z)(3x)2 + y2 + z2 – 3xy – yz – 3xz
= (3x + y + z)(9x2 + y2 + z2 – 3xy – yz – 3xz)
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