Solve 81m^4/100-n^2/36

$$\frac { 81 m ^ { 4 } } { 100 } - \frac { n ^ { 2 } } { 36 }$$

Factor

$$\frac{\left(27m^{2}-5n\right)\left(27m^{2}+5n\right)}{900}$$

Solution Steps

Factor out \frac{1}{900}.

$$\frac{729m^{4}-25n^{2}}{900}$$

Consider 729m^{4}-25n^{2}. Rewrite 729m^{4}-25n^{2} as \left(27m^{2}\right)^{2}-\left(5n\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(27m^{2}-5n\right)\left(27m^{2}+5n\right)$$

Rewrite the complete factored expression.

$$\frac{\left(27m^{2}-5n\right)\left(27m^{2}+5n\right)}{900}$$

Evaluate

$$\frac{81m^{4}}{100}-\frac{n^{2}}{36}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 100 and 36 is 900. Multiply \frac{81m^{4}}{100} times \frac{9}{9}. Multiply \frac{n^{2}}{36} times \frac{25}{25}.

$$\frac{9\times 81m^{4}}{900}-\frac{25n^{2}}{900}$$

Since \frac{9\times 81m^{4}}{900} and \frac{25n^{2}}{900} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9\times 81m^{4}-25n^{2}}{900}$$

Do the multiplications in 9\times 81m^{4}-25n^{2}.

$$\frac{729m^{4}-25n^{2}}{900}$$