Solve 162/n^2nleft(2n+1right)left(n+1right)/6

$$\frac{ 162 }{ { n }^{ 2 } } \frac{ n \left( 2n+1 \right) \left( n+1 \right) }{ 6 }$$

Evaluate

$$54n+81+\frac{27}{n}$$

Short Solution Steps

Use the distributive property to multiply n by 2n+1.

$$\frac{162}{n^{2}}\times \frac{\left(2n^{2}+n\right)\left(n+1\right)}{6}$$

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

$$\frac{162}{n^{2}}\times \frac{2n^{3}+3n^{2}+n}{6}$$

Multiply \frac{162}{n^{2}} times \frac{2n^{3}+3n^{2}+n}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{162\left(2n^{3}+3n^{2}+n\right)}{n^{2}\times 6}$$

Cancel out 6 in both numerator and denominator.

$$\frac{27\left(2n^{3}+3n^{2}+n\right)}{n^{2}}$$

Factor the expressions that are not already factored.

$$\frac{27n\left(n+1\right)\left(2n+1\right)}{n^{2}}$$

Cancel out n in both numerator and denominator.

$$\frac{27\left(n+1\right)\left(2n+1\right)}{n}$$

Expand the expression.

$$\frac{54n^{2}+81n+27}{n}$$

Expand

$$54n+81+\frac{27}{n}$$

Short Solution Steps

Use the distributive property to multiply n by 2n+1.

$$\frac{162}{n^{2}}\times \frac{\left(2n^{2}+n\right)\left(n+1\right)}{6}$$

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

$$\frac{162}{n^{2}}\times \frac{2n^{3}+3n^{2}+n}{6}$$

Multiply \frac{162}{n^{2}} times \frac{2n^{3}+3n^{2}+n}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{162\left(2n^{3}+3n^{2}+n\right)}{n^{2}\times 6}$$

Cancel out 6 in both numerator and denominator.

$$\frac{27\left(2n^{3}+3n^{2}+n\right)}{n^{2}}$$

Factor the expressions that are not already factored.

$$\frac{27n\left(n+1\right)\left(2n+1\right)}{n^{2}}$$

Cancel out n in both numerator and denominator.

$$\frac{27\left(n+1\right)\left(2n+1\right)}{n}$$

Expand the expression.

$$\frac{54n^{2}+81n+27}{n}$$