Solve m^3/64+n^3/125

$$\frac { m ^ { 3 } } { 64 } + \frac { n ^ { 3 } } { 125 }$$

Factor

$$\frac{\left(5m+4n\right)\left(25m^{2}-20mn+16n^{2}\right)}{8000}$$

Solution Steps

Factor out \frac{1}{8000}.

$$\frac{125m^{3}+64n^{3}}{8000}$$

Consider 125m^{3}+64n^{3}. Rewrite 125m^{3}+64n^{3} as \left(5m\right)^{3}+\left(4n\right)^{3}. The sum of cubes can be factored using the rule: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).

$$\left(5m+4n\right)\left(25m^{2}-20mn+16n^{2}\right)$$

Rewrite the complete factored expression.

$$\frac{\left(5m+4n\right)\left(25m^{2}-20mn+16n^{2}\right)}{8000}$$

Evaluate

$$\frac{m^{3}}{64}+\frac{n^{3}}{125}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 64 and 125 is 8000. Multiply \frac{m^{3}}{64} times \frac{125}{125}. Multiply \frac{n^{3}}{125} times \frac{64}{64}.

$$\frac{125m^{3}}{8000}+\frac{64n^{3}}{8000}$$

Since \frac{125m^{3}}{8000} and \frac{64n^{3}}{8000} have the same denominator, add them by adding their numerators.

$$\frac{125m^{3}+64n^{3}}{8000}$$