Question

factorise.. 8 xcube + 27 ycube +64 zcube -72xyz

Answer 1

$8 {x}^{3 } + 27 {y}^{3} + 64 {z}^{3} - 72xyz \\ \\ (factorise \: using \: {x}^{3} + {y}^{3} + {z}^{3} - 3xyz = (x + y + z)( {x}^{2} + {y}^{2} + {z}^{2} - xy - yz - xz) \\ \\ = {(2x)}^{3} + {(3y)}^{3} + {(4z)}^{3} - 3 \times (2x \times 3y \times 4z) \\ = (2x + 3y + 4z)(4 {x}^{2} + 9 {y}^{2} + 16{z}^{2} - 6xy - 12yz - 8xz)$

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