# How do you multiply (-3t^2+4t-7)(-2t)?

Jun 25, 2015

$\left(- 3 {t}^{2} + 4 t - 7\right) \left(- 2 t\right)$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$= 6 {t}^{3} - 8 {t}^{2} + 14 t$

#### Explanation:

The Distributive Property (of Multiplication over Addition) tells us:
$\textcolor{w h i t e}{\text{XXXX}}$$\left(a + b + c\right) \times \left(d\right) = a d + b d + c d$

So $\left(- 3 {t}^{2} + 4 t - 7\right) \left(- 2 t\right)$
$\textcolor{w h i t e}{\text{XXXX}}$$= \left(- 3 {t}^{2}\right) \cdot \left(- 2 t\right) + \left(4 t\right) \cdot \left(- 2 t\right) - \left(7\right) \cdot \left(- 2 t\right)$

$\textcolor{w h i t e}{\text{XXXX}}$$= 6 {t}^{3} - 8 {t}^{2} + 14 t$