Factorise: 27x3+y3+z3–9xy.
Solution and Explanation
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 - (3x)(y) - (y)(z) - z(3x)]
= (3x + y + z) [9x2 + y2 + z2 - 3xy - yz - 3xz]
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