Solve (1/20c^5-3/5c^4+3/10c^3)div(1/100c^3)

$$( \frac { 1 } { 20 } c ^ { 5 } - \frac { 3 } { 5 } c ^ { 4 } + \frac { 3 } { 10 } c ^ { 3 } ) \div ( \frac { 1 } { 100 } c ^ { 3 } )$$

Evaluate

$$5\left(c^{2}-12c+6\right)$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\frac{1}{20}\left(c-\left(\sqrt{30}+6\right)\right)\left(c-\left(-\sqrt{30}+6\right)\right)c^{3}}{\frac{1}{100}c^{3}}$$

Cancel out c^{3} in both numerator and denominator.

$$\frac{\frac{1}{20}\left(c-\left(\sqrt{30}+6\right)\right)\left(c-\left(-\sqrt{30}+6\right)\right)}{\frac{1}{100}}$$

Expand the expression.

$$\frac{\frac{1}{20}c^{2}-\frac{3}{5}c+\frac{3}{10}}{\frac{1}{100}}$$

Divide \frac{1}{20}c^{2}-\frac{3}{5}c+\frac{3}{10} by \frac{1}{100} by multiplying \frac{1}{20}c^{2}-\frac{3}{5}c+\frac{3}{10} by the reciprocal of \frac{1}{100}.

$$\left(\frac{1}{20}c^{2}-\frac{3}{5}c+\frac{3}{10}\right)\times 100$$

Use the distributive property to multiply \frac{1}{20}c^{2}-\frac{3}{5}c+\frac{3}{10} by 100.

$$5c^{2}-60c+30$$

Expand

$$5c^{2}-60c+30$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\frac{1}{20}\left(c-\left(\sqrt{30}+6\right)\right)\left(c-\left(-\sqrt{30}+6\right)\right)c^{3}}{\frac{1}{100}c^{3}}$$

Cancel out c^{3} in both numerator and denominator.

$$\frac{\frac{1}{20}\left(c-\left(\sqrt{30}+6\right)\right)\left(c-\left(-\sqrt{30}+6\right)\right)}{\frac{1}{100}}$$

Expand the expression.

$$\frac{\frac{1}{20}c^{2}-\frac{3}{5}c+\frac{3}{10}}{\frac{1}{100}}$$

Divide \frac{1}{20}c^{2}-\frac{3}{5}c+\frac{3}{10} by \frac{1}{100} by multiplying \frac{1}{20}c^{2}-\frac{3}{5}c+\frac{3}{10} by the reciprocal of \frac{1}{100}.

$$\left(\frac{1}{20}c^{2}-\frac{3}{5}c+\frac{3}{10}\right)\times 100$$

Use the distributive property to multiply \frac{1}{20}c^{2}-\frac{3}{5}c+\frac{3}{10} by 100.

$$5c^{2}-60c+30$$