How do you multiply $- 2 x y z (3 x^{2} + 2 y^{2} + z^{2} - 4 w^{2})$ $-2xyz(3x^2+2y^2+z^2-4w^2)$ ?

Question

1980 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-13T14:05:15

$- 6 x^{3} y z - 4 x y^{3} z - 2 x y z^{3} + 8 w^{2} x y z$ $-6x^3yz -4xy^3z -2xyz^3+8w^2xyz$

Use the distributive law to multiply the factor outside by each of the terms inside the bracket,.

Multiply:
the signs, then the numbers, then add the indices of like bases.

$- 2 x y z (3 x^{2} + 2 y^{2} + z^{2} - 4 w^{2})$ $-2xyz(3x^2+2y^2+z^2-4w^2)$

$- 6 x^{3} y z - 4 x y^{3} z - 2 x y z^{3} + 8 w^{2} x y z$ $-6x^3yz -4xy^3z -2xyz^3+8w^2xyz$

There are four terms in the bracket so there should be four terms in the final answer.

Answer 2 · 2017-05-13T14:55:08

$8 w^{2} x y z - 6 x^{3} y z - 4 x y^{3} z - 2 x y z^{3}$ $8w^2xyz-6x^3yz-4xy^3z-2xyz^3$

$- 2 x y z (3 x^{2} + 2 y^{2} + z^{2} - 4 w^{2})$ $-2xyz(color(blue)(3x^2+2y^2+z^2-4w^2))$

$:.=color(blue)(3x^2)(-2xyz)+color(blue)(2y^2)(-2xyz)+color(blue)(z^2)(-2xyz)-color(blue)(4w^2)(-2xyz)$

$:.=(-6x^3yz-4xy^3z-2xyz^2+8w^2xyz)$

$:.=color(blue)(8w^2xyz-6x^3yz-4xy^3z-2xyz^3$

How do you multiply -2xyz(3x^2+2y^2+z^2-4w^2)−2xyz(3x2+2y2+z2−4w2)-2xyz(3x^2+2y^2+z^2-4w^2)?