The product of $(2 x - 3 y + 5 z)$ and $(4 x^{2} + 9 y^{2} + 25 z^{2} + 6 x y + 15 y z - 10 x z)$ is

8 x^{3} - 27 y^{3} - 125 z^{3} - 90 x y z

No worries! We‘ve got your back. Try BYJU‘S free classes today!

8 x^{3} - 27 y^{3} + 125 z^{3} - 90 x y z

No worries! We‘ve got your back. Try BYJU‘S free classes today!

8 x^{3} + 27 y^{3} - 125 z^{3} + 90 x y z

No worries! We‘ve got your back. Try BYJU‘S free classes today!

8 x^{3} - 27 y^{3} + 125 z^{3} + 90 x y z

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $8 x^{3} - 27 y^{3} + 125 z^{3} + 90 x y z$
$(2 x - 3 y + 5 z) (4 x^{2} + 9 y^{2} + 25 z^{2} + 6 x y + 15 z - 10 x z)$
$= (2 x - 3 y + 5 z) [(2 x)^{2} + (3 y)^{2} + (5 z)^{2} - (2 x) (- 3 y) - (- 3 y) (5 z) - (2 x) (5 z)]$
Using formula $(x + y + z) (x^{2} + y^{2} + z^{2} - x y - y z - z x) = x^{3} + y^{3} + z^{3} - 3 x y z$
$= (2 x)^{3} + (- 3 y)^{3} + (5 z)^{3} - 3.2 x . (- 3 y) .5 z$
$= (2 x)^{3} + (- 3 y)^{3} + (5 z)^{3} + 90 x y z$

Suggest Corrections