# How do you multiply (-2z^2 + 6z - 1)(- 4z^2)?

Apr 10, 2015

We use the Distributive Property of Multiplication to solve this.

In general, color(blue)((a+-b)*c = (a*b) +- (a*c)

$\left(- 2 {z}^{2} + 6 z - 1\right) \left(- 4 {z}^{2}\right)$

$= \left(- 2 {z}^{2}\right) \cdot \left(- 4 {z}^{2}\right) + 6 z \left(- 4 {z}^{2}\right) - \left(- 4 {z}^{2}\right)$

$= \left(- 2 \cdot - 4\right) \left({z}^{2} \cdot {z}^{2}\right) + \left(6 \cdot \left(- 4\right)\right) \left(z \cdot {z}^{2}\right) + 4 {z}^{2}$

In general,color(blue)( a^m*a^n = a^(m+n)

$= \left(8\right) \left({z}^{2 + 2}\right) + 6 \left(- 4\right) \left({z}^{1 + 2}\right) + 4 {z}^{2}$

$= 8 {z}^{4} + \left(- 24\right) \left({z}^{3}\right) + 4 {z}^{2}$

color(green)(= 8z^4 - 24z^3 + 4z^2