# How do you find the product (6z^2-5z-2)(3z^3-2z-4)?

Apr 15, 2017

$18 {z}^{5} - 18 {z}^{3} - 29 {z}^{2} + 24 z + 8$

#### Explanation:

Given -

$\left(6 {z}^{2} - 5 z - 2\right) \left(3 {z}^{3} - 2 z - 4\right)$

Multiply each term in the expression $\left(6 {z}^{2} - 5 z - 2\right)$ with $3 {z}^{3}$

$18 {z}^{5} - 15 {z}^{2} - 6 {z}^{3}$

Multiply each term in the expression $\left(6 {z}^{2} - 5 z - 2\right)$ with $- 2 z$

$18 {z}^{5} - 15 {z}^{2} - 6 {z}^{3} - 12 {z}^{3} + 10 {z}^{2} + 4 z$

Multiply each term in the expression $\left(6 {z}^{2} - 5 z - 2\right)$ with $- 4$

$18 {z}^{5} - 15 {z}^{2} - 6 {z}^{3} - 12 {z}^{3} + 10 {z}^{2} + 4 z - 24 {z}^{2} + 20 z + 8$

Group all the like terms

$18 {z}^{5} - 6 {z}^{3} - 12 {z}^{3} - 15 {z}^{2} + 10 {z}^{2} - 24 {z}^{2} + 4 z + 20 z + 8$

Simplify

$18 {z}^{5} - 18 {z}^{3} - 29 {z}^{2} + 24 z + 8$