Solve 1/4ab^4-36/25a^5

$$\frac { 1 } { 4 } a b ^ { 4 } - \frac { 36 } { 25 } a ^ { 5 }$$

Factor

$$\frac{a\left(5b^{2}-12a^{2}\right)\left(12a^{2}+5b^{2}\right)}{100}$$

Solution Steps

Factor out \frac{1}{100}.

$$\frac{25ab^{4}-144a^{5}}{100}$$

Consider 25ab^{4}-144a^{5}. Factor out a.

$$a\left(25b^{4}-144a^{4}\right)$$

Consider 25b^{4}-144a^{4}. Rewrite 25b^{4}-144a^{4} as \left(5b^{2}\right)^{2}-\left(12a^{2}\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(5b^{2}-12a^{2}\right)\left(5b^{2}+12a^{2}\right)$$

Reorder the terms.

$$\left(-12a^{2}+5b^{2}\right)\left(12a^{2}+5b^{2}\right)$$

Rewrite the complete factored expression.

$$\frac{a\left(-12a^{2}+5b^{2}\right)\left(12a^{2}+5b^{2}\right)}{100}$$

Evaluate

$$\frac{ab^{4}}{4}-\frac{36a^{5}}{25}$$