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Difference of Two Squares

Factorise: ...

Question

Factorise: $x^{3} - 8 y^{3} - 64 z^{3} - 24 x y z$ using identity ?

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Solution

Given,
$x^{3} - {8 y}^{3} - {64 z}^{3} - 24 x y z = {(x)}^{3} + {(- 2 y)}^{3} + {(- 4 z)}^{3} - 3 (x) (- 2 y) (- 4 z) = (x - 2 y - 4 z) [x^{2} + {(- 2 y)}^{2} + {(- 4 z)}^{2} - x (- 2 y) (- 4 z) - (- 4 z) x] = (x - 2 y - 4 z) (x^{2} + {4 y}^{2} + {16 z}^{2} + 2 x y - 8 y z + 4 z x) .$

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Difference of Two Squares

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