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

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

Evaluate

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

Solution Steps

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

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

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

$$\frac{3}{2}\left(-a^{2}\right)+\frac{9}{2}a-\frac{1}{2}a\left(-a^{2}\right)-\frac{3}{2}a^{2}$$

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

$$\frac{3}{2}\left(-a^{2}\right)+\frac{9}{2}a+\frac{1}{2}aa^{2}-\frac{3}{2}a^{2}$$

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

$$\frac{3}{2}\left(-a^{2}\right)+\frac{9}{2}a+\frac{1}{2}a^{3}-\frac{3}{2}a^{2}$$

Multiply \frac{3}{2} and -1 to get -\frac{3}{2}.

$$-\frac{3}{2}a^{2}+\frac{9}{2}a+\frac{1}{2}a^{3}-\frac{3}{2}a^{2}$$

Combine -\frac{3}{2}a^{2} and -\frac{3}{2}a^{2} to get -3a^{2}.

$$-3a^{2}+\frac{9}{2}a+\frac{1}{2}a^{3}$$

Expand

$$\frac{a^{3}}{2}-3a^{2}+\frac{9a}{2}$$

Solution Steps

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

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

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

$$\frac{3}{2}\left(-a^{2}\right)+\frac{9}{2}a-\frac{1}{2}a\left(-a^{2}\right)-\frac{3}{2}a^{2}$$

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

$$\frac{3}{2}\left(-a^{2}\right)+\frac{9}{2}a+\frac{1}{2}aa^{2}-\frac{3}{2}a^{2}$$

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

$$\frac{3}{2}\left(-a^{2}\right)+\frac{9}{2}a+\frac{1}{2}a^{3}-\frac{3}{2}a^{2}$$

Multiply \frac{3}{2} and -1 to get -\frac{3}{2}.

$$-\frac{3}{2}a^{2}+\frac{9}{2}a+\frac{1}{2}a^{3}-\frac{3}{2}a^{2}$$

Combine -\frac{3}{2}a^{2} and -\frac{3}{2}a^{2} to get -3a^{2}.

$$-3a^{2}+\frac{9}{2}a+\frac{1}{2}a^{3}$$