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

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

Evaluate

$$\frac{\left(3-n\right)\left(n^{2}-6n+1\right)n^{3}}{4}$$

Solution Steps

Use the distributive property to multiply -\frac{1}{2}n^{3}+\frac{3}{2}n^{2} by -3n^{2}+\frac{1}{2}n+\frac{1}{2}n^{3} and combine like terms.

$$\frac{9}{4}n^{5}-\frac{19}{4}n^{4}-\frac{1}{4}n^{6}+\frac{3}{4}n^{3}$$

Expand

$$\frac{3n^{3}-19n^{4}+9n^{5}-n^{6}}{4}$$

Solution Steps

Use the distributive property to multiply -\frac{1}{2}n^{3}+\frac{3}{2}n^{2} by -3n^{2}+\frac{1}{2}n+\frac{1}{2}n^{3} and combine like terms.

$$\frac{9}{4}n^{5}-\frac{19}{4}n^{4}-\frac{1}{4}n^{6}+\frac{3}{4}n^{3}$$