Factorize: 27x3 + y3 + z3 – 9xyz
Concept Used:
x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – xz)
Explanation:
27x3 + y3 + z3 – 9xyz = (3x)3 + y3 + z3 – 3 × 3xyz
Using identity,
x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – xz)
27x3 + y3 + z3 – 9xyz
= (3x + y + z) {(3x)2 + y2 + z2 – 3xy – yz – 3xz}
= (3x + y + z) (9x2 + y2 + z2 – 3xy – yz – 3xz)
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Generated by AI. May contain inaccuracies — always verify with your textbook.
