Factorize the following expression:
$x^{3} + 8 y^{3} + 64 z^{3} - 24 x y z$

Open in App

Solution

Factorizing the given expression:
$x^{3} + 8 y^{3} + 64 z^{3} - 24 x y z = x^{3} + {(2 y)}^{3} + {(4 z)}^{3} - 3 \times x \times 2 y \times 4 z = (x + 2 y + 4 z) (x^{2} + 4 y^{2} + 16 z^{2} - 2 x y - 8 y z - 4 x z) [U \sin g t h e i d e n t i t y a^{3} + b^{3} + c^{3} - 3 a b c = (a + b + c) (a^{2} + b^{2} + c^{2} - a b - b c - c a)]$
Hence, after factorizing we get $x^{3} + 8 y^{3} + 64 z^{3} - 24 x y z = (x + 2 y + 4 z) (x^{2} + 4 y^{2} + 16 z^{2} - 2 x y - 8 y z - 4 x z) .$

Suggest Corrections

Similar questions

x^{3} - 8 y^{3} - 64 z^{3} - 24 x y z

Factorize $x^{3} - 8 y^{3} + 27 z^{3} + 18 x y z$

Join BYJU'S Learning Program