Solve =1/6n(n+1)(6n^2+14n-5)

$$= \frac { 1 } { 6 } n ( n + 1 ) ( 6 n ^ { 2 } + 14 n - 5 )$$

Evaluate

$$\frac{n\left(n+1\right)\left(6n^{2}+14n-5\right)}{6}$$

Solution Steps

Use the distributive property to multiply \frac{1}{6}n by n+1.

$$\left(\frac{1}{6}n^{2}+\frac{1}{6}n\right)\left(6n^{2}+14n-5\right)$$

Use the distributive property to multiply \frac{1}{6}n^{2}+\frac{1}{6}n by 6n^{2}+14n-5 and combine like terms.

$$n^{4}+\frac{10}{3}n^{3}+\frac{3}{2}n^{2}-\frac{5}{6}n$$

Expand

$$n^{4}+\frac{10n^{3}}{3}+\frac{3n^{2}}{2}-\frac{5n}{6}$$

Solution Steps

Use the distributive property to multiply \frac{1}{6}n by n+1.

$$\left(\frac{1}{6}n^{2}+\frac{1}{6}n\right)\left(6n^{2}+14n-5\right)$$

Use the distributive property to multiply \frac{1}{6}n^{2}+\frac{1}{6}n by 6n^{2}+14n-5 and combine like terms.

$$n^{4}+\frac{10}{3}n^{3}+\frac{3}{2}n^{2}-\frac{5}{6}n$$