Question

factorise 27 x cube + y cube + Z cube minus 9 x y z​

Answer 1

Answer:

Here's Your Answer :-

$27 {x}^{3} + {y}^{3} + {z}^{3} - 3xyz \\ = (3x + y + z) (9 {x}^{2} + {y}^{2} + {z}^{2} - 3xy \\ - yz - 3zx$

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Answer 2

Answer:

$(3x + y + z)(9 {x}^{2} + {y}^{2} + {z}^{2} - 3xy - yz - 3xz)$

Explanation:

$27 {x}^{3} + {y}^{3} + {z}^{3} - 9xyz \\ = {(3x)}^{3} + {y}^{3} + {z}^{3} - 3(3x)(y)(z)$

According to the formula,

${x}^{3} + {y}^{3} + {z}^{3} - 3xyz = (x + y + z)( {x}^{2} + {y}^{2} + {z}^{2} - xy - yz - xz) \\ = (3x + y + z)( {(3x)}^{2} + {y}^{2} + {z}^{2} - 3xy - yz - 3xz) \\ = (3x + y + z)(9 {x}^{2} + {y}^{2} + {z}^{2} - 3xy - yz - 3xz)$

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