Question

factorise : x3-27y3 + 8z3 + 18xyz

please help​

Answer 1

Use of identity

$\tt \:  ⟼ {x}^{3} + {y}^{3} + {z}^{3} - 3xyz \: =$

$\tt \:  (x + y + z)({x}^{2} + {y}^{2} + {z}^{2} - xy - yz - zx)$

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$\tt \:  ⟼ \: factorise : \: {x}^{3} - {27y}^{3} + {8z}^{3} + 18xyz$

$\tt \:  = {(x)}^{3} + {( - 3y)}^{3} + {(2z)}^{3} - 3(x)( - 3y)(2z)$

$\tt \:  = (x - 3y + 2z) \bigg( {x}^{2} + {( - 3y)}^{2} + {(2z)}^{2} - x( - 3y) - ( - 3y)(2z) - (2z)(x) \bigg)$

$\tt \:  = (x - 3y + 2z)( {x}^{2} + {9y}^{2} + {4z}^{2} + 3xy + 6yz - 2xz)$