Factorise $27 x^{3} + y^{3} + z^{3} - 9 x y z$ [2 MARKS]

Open in App

Solution

Formula: 1 Mark
Substitution & Simplication: 1 Mark

$x^{3} + y^{3} + z^{3} - 3 x y z$
$= (x + y + z) (x^{2} + y^{2} + z^{2} - x y - y z - z x)$
Comparing from above identity

$= {(3 x)}^{3} + y^{3} + z^{3} - 3 (3 x) y z$

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

$= (3 x + y + z) ({9 x}^{2} + y^{2} + z^{2} - 3 x y - y z - 3 z x)$

Suggest Corrections

Similar questions

27 x^{3} + y^{3} + z^{3} - 9 x y z

27 x^{3} + y^{3} + z^{3} - 9 x y z

Factorise: $27 x^{3} + y^{3} + z^{3} - 9 x y z$

Join BYJU'S Learning Program