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

May 13, 2017

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

Explanation:

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.

$- 2 x y z \left(3 {x}^{2} + 2 {y}^{2} + {z}^{2} - 4 {w}^{2}\right)$

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

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

May 13, 2017

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

Explanation:

$- 2 x y z \left(\textcolor{b l u e}{3 {x}^{2} + 2 {y}^{2} + {z}^{2} - 4 {w}^{2}}\right)$

$\therefore = \textcolor{b l u e}{3 {x}^{2}} \left(- 2 x y z\right) + \textcolor{b l u e}{2 {y}^{2}} \left(- 2 x y z\right) + \textcolor{b l u e}{{z}^{2}} \left(- 2 x y z\right) - \textcolor{b l u e}{4 {w}^{2}} \left(- 2 x y z\right)$

$\therefore = \left(- 6 {x}^{3} y z - 4 x {y}^{3} z - 2 x y {z}^{2} + 8 {w}^{2} x y z\right)$

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