Solve a^4/36-x^6/25

$$\frac { a ^ { 4 } } { 36 } - \frac { x ^ { 6 } } { 25 }$$

Evaluate

$$-\frac{x^{6}}{25}+\frac{a^{4}}{36}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 36 and 25 is 900. Multiply \frac{a^{4}}{36} times \frac{25}{25}. Multiply \frac{x^{6}}{25} times \frac{36}{36}.

$$\frac{25a^{4}}{900}-\frac{36x^{6}}{900}$$

Since \frac{25a^{4}}{900} and \frac{36x^{6}}{900} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25a^{4}-36x^{6}}{900}$$

Factor

$$\frac{\left(5a^{2}-6x^{3}\right)\left(6x^{3}+5a^{2}\right)}{900}$$

Solution Steps

Factor out \frac{1}{900}.

$$\frac{25a^{4}-36x^{6}}{900}$$

Consider 25a^{4}-36x^{6}. Rewrite 25a^{4}-36x^{6} as \left(5a^{2}\right)^{2}-\left(6x^{3}\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(5a^{2}-6x^{3}\right)\left(5a^{2}+6x^{3}\right)$$

Reorder the terms.

$$\left(-6x^{3}+5a^{2}\right)\left(6x^{3}+5a^{2}\right)$$

Rewrite the complete factored expression.

$$\frac{\left(-6x^{3}+5a^{2}\right)\left(6x^{3}+5a^{2}\right)}{900}$$