Mathematics
Factorise : 27x3 + y3 + z3 - 9xyz
Polynomials
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Answer
27x3 + y3 + z3 - 9xyz
[∵ x3 + y3 + z3 - 3xyz = (x + y + z)(x2 + y2 + z2 - xy - yz - zx)]
= (3x)3 + y3 + z3 - 3(3x)(y)(z)
= (3x + y + z)[(3x)2 + y2 + z2 - (3x)(y) - (y)(z) - (z)(3x)]
= (3x + y + z)(9x2 + y2 + z2 - 3xy - yz - 3zx)
Hence, 27x3 + y3 + z3 - 9xyz = (3x + y + z)(9x2 + y2 + z2 - 3xy - yz - 3zx)
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