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

Apr 8, 2017

Use the distributive property of multiplication.

#### Explanation:

The first terms in each parentheses are multiplied by each other. Then the ‘outer’ and ‘inner’ pairs are multiplied and added to each other. Finally, the last terms in each parentheses are multiplied together. The final result may be simplified.

 (a^2+3a)(−a^2+2a)

Step 1. ${a}^{2} \cdot - {a}^{2} = - {a}^{4}$

Step 2. $\left({a}^{2} \cdot 2 a\right) + \left(3 a \cdot - {a}^{2}\right) = 2 {a}^{3} - 3 {a}^{3}$ ; $- {a}^{3}$

Step 3. $3 a \cdot 2 a = 6 {a}^{2}$

Step 4. $- {a}^{4} - {a}^{3} + 6 {a}^{2}$

Apr 8, 2017

$- {a}^{4} - {a}^{3} + 6 {a}^{2}$

#### Explanation:

Multiply using F.O.I.L

F: $\left(\textcolor{red}{{a}^{2}} + 3 a\right) \left(\textcolor{red}{- {a}^{2}} + 2 a\right) \to \textcolor{red}{- {a}^{4}}$
O: (color(red)(a^2)+3a)(-a^2+color(red)(2a)) -> color(red)(2a^3
I: (a^2+color(red)(3a))(color(red)(-a^2)+2a) ->color(red)( -3a^3
L: $\left({a}^{2} + \textcolor{red}{3 a}\right) \left(- {a}^{2} + \textcolor{red}{2 a}\right) \to \textcolor{red}{6 {a}^{2}}$

Now by combining like terms we end up with:

$- {a}^{4} - {a}^{3} + 6 {a}^{2}$