Solve 4p^3/5+7-3p^3/10-11=

$$\frac { 4 p ^ { 3 } } { 5 } + 7 - \frac { 3 p ^ { 3 } } { 10 } - 11 =$$

Evaluate

$$\frac{p^{3}}{2}-4$$

Short Solution Steps

Subtract 11 from 7 to get -4.

$$\frac{4p^{3}}{5}-4-\frac{3p^{3}}{10}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{5}{5}.

$$\frac{4p^{3}}{5}-\frac{4\times 5}{5}-\frac{3p^{3}}{10}$$

Since \frac{4p^{3}}{5} and \frac{4\times 5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4p^{3}-4\times 5}{5}-\frac{3p^{3}}{10}$$

Do the multiplications in 4p^{3}-4\times 5.

$$\frac{4p^{3}-20}{5}-\frac{3p^{3}}{10}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 10 is 10. Multiply \frac{4p^{3}-20}{5} times \frac{2}{2}.

$$\frac{2\left(4p^{3}-20\right)}{10}-\frac{3p^{3}}{10}$$

Since \frac{2\left(4p^{3}-20\right)}{10} and \frac{3p^{3}}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(4p^{3}-20\right)-3p^{3}}{10}$$

Do the multiplications in 2\left(4p^{3}-20\right)-3p^{3}.

$$\frac{8p^{3}-40-3p^{3}}{10}$$

Combine like terms in 8p^{3}-40-3p^{3}.

$$\frac{5p^{3}-40}{10}$$

Factor

$$\frac{\left(p-2\right)\left(p^{2}+2p+4\right)}{2}$$

Solution Steps

Factor out \frac{1}{10}.

$$\frac{5p^{3}-40}{10}$$

Consider 8p^{3}+70-3p^{3}-110. Multiply and combine like terms.

$$5p^{3}-40$$

Consider 5p^{3}-40. Factor out 5.

$$5\left(p^{3}-8\right)$$

Consider p^{3}-8. Rewrite p^{3}-8 as p^{3}-2^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

$$\left(p-2\right)\left(p^{2}+2p+4\right)$$

Rewrite the complete factored expression.

$$\frac{\left(p-2\right)\left(p^{2}+2p+4\right)}{2}$$