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

FOIL to get
$3 {t}^{5} - 2 {t}^{4} - 9 {t}^{3} + 6 {t}^{2}$

#### Explanation:

To do the multiplication, we use FOIL - which gives an order to multiplying terms within brackets. In essence, we just want to make sure that everything inside one bracket gets multiplied by everything in the other bracket, like this:

$- {t}^{3} \cdot - 3 {t}^{2} = 3 {t}^{5}$
$- {t}^{3} \cdot 2 t = - 2 {t}^{4}$
$3 t \cdot - 3 {t}^{2} = - 9 {t}^{3}$
$3 t \cdot 2 t = 6 {t}^{2}$

And now we add them all up:

$3 {t}^{5} - 2 {t}^{4} - 9 {t}^{3} + 6 {t}^{2}$