Solve 1/5m^3-5/7n^4-7/10m^3+2n^4

$$\frac { 1 } { 5 } m ^ { 3 } - \frac { 5 } { 7 } n ^ { 4 } - \frac { 7 } { 10 } m ^ { 3 } + 2 n ^ { 4 }$$

Evaluate

$$\frac{9n^{4}}{7}-\frac{m^{3}}{2}$$

Solution Steps

Combine \frac{1}{5}m^{3} and -\frac{7}{10}m^{3} to get -\frac{1}{2}m^{3}.

$$-\frac{1}{2}m^{3}-\frac{5}{7}n^{4}+2n^{4}$$

Combine -\frac{5}{7}n^{4} and 2n^{4} to get \frac{9}{7}n^{4}.

$$-\frac{1}{2}m^{3}+\frac{9}{7}n^{4}$$

Factor

$$\frac{18n^{4}-7m^{3}}{14}$$

Solution Steps

Factor out \frac{1}{70}.

$$\frac{14m^{3}-50n^{4}-49m^{3}+140n^{4}}{70}$$

Consider 14m^{3}-50n^{4}-49m^{3}+140n^{4}. Multiply and combine like terms.

$$-35m^{3}+90n^{4}$$

Consider -35m^{3}+90n^{4}. Factor out 5.

$$5\left(-7m^{3}+18n^{4}\right)$$

Rewrite the complete factored expression.

$$\frac{-7m^{3}+18n^{4}}{14}$$