Solve 1/2a*(-a^2+3a)

$$\frac { 1 } { 2 } a \times ( - a ^ { 2 } + 3 a )$$

Evaluate

$$\frac{\left(3-a\right)a^{2}}{2}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2}a by -a^{2}+3a.

$$\frac{1}{2}a\left(-a^{2}\right)+\frac{3}{2}a^{2}$$

Multiply \frac{1}{2} and -1 to get -\frac{1}{2}.

$$-\frac{1}{2}aa^{2}+\frac{3}{2}a^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$-\frac{1}{2}a^{3}+\frac{3}{2}a^{2}$$

Expand

$$\frac{3a^{2}-a^{3}}{2}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2}a by -a^{2}+3a.

$$\frac{1}{2}a\left(-a^{2}\right)+\frac{3}{2}a^{2}$$

Multiply \frac{1}{2} and -1 to get -\frac{1}{2}.

$$-\frac{1}{2}aa^{2}+\frac{3}{2}a^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$-\frac{1}{2}a^{3}+\frac{3}{2}a^{2}$$