Solve 1/6(n-1)(n^2+n+6)+1

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

Evaluate

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

Solution Steps

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

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

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

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

Add -1 and 1 to get 0.

$$\frac{1}{6}n^{3}+\frac{5}{6}n$$

Expand

$$\frac{n^{3}+5n}{6}$$

Solution Steps

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

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

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

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

Add -1 and 1 to get 0.

$$\frac{1}{6}n^{3}+\frac{5}{6}n$$