Solve 25/4-r^2/9

$$\frac { 25 } { 4 } - \frac { r ^ { 2 } } { 9 }$$

Evaluate

$$-\frac{r^{2}}{9}+\frac{25}{4}$$

Short Solution Steps

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

$$\frac{25\times 9}{36}-\frac{4r^{2}}{36}$$

Since \frac{25\times 9}{36} and \frac{4r^{2}}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25\times 9-4r^{2}}{36}$$

Do the multiplications in 25\times 9-4r^{2}.

$$\frac{225-4r^{2}}{36}$$

Factor

$$\frac{\left(-2r-15\right)\left(2r-15\right)}{36}$$

Solution Steps

Factor out \frac{1}{36}.

$$\frac{225-4r^{2}}{36}$$

Consider 225-4r^{2}. Rewrite 225-4r^{2} as 15^{2}-\left(2r\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(15-2r\right)\left(15+2r\right)$$

Reorder the terms.

$$\left(-2r+15\right)\left(2r+15\right)$$

Rewrite the complete factored expression.

$$\frac{\left(-2r+15\right)\left(2r+15\right)}{36}$$