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Question

Factorise: 27x3+y3+z3-9xyz


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Solution

Factorization

The given equation is,

27x3+y3+z3-9xyz=(3x)3+y3+z3-3(3xyz)

We know that,

a3+b3+c3-3abc=(a+b+c)(a2+b2+c2-ab-bc-ca)

27x3+y3+z3-9xyz=(3x+y+z)(9x2+y2+z2-3xy-yz-3xz)

Hence, the result of factorization of the given expression is (3x+y+z)(9x2+y2+z2-3xy-yz-3xz).


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