Q. 174.4( 57 Votes )

Factorize: 27x3 + y3 + z3 – 9xyz

Answer :

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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