Solve (5/2-r/3)(5/2+r/3)

$$( \frac { 5 } { 2 } - \frac { r } { 3 } ) ( \frac { 5 } { 2 } + \frac { r } { 3 } )$$

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 2 and 3 is 6. Multiply \frac{5}{2} times \frac{3}{3}. Multiply \frac{r}{3} times \frac{2}{2}.

$$\left(\frac{5\times 3}{6}-\frac{2r}{6}\right)\left(\frac{5}{2}+\frac{r}{3}\right)$$

Since \frac{5\times 3}{6} and \frac{2r}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\times 3-2r}{6}\left(\frac{5}{2}+\frac{r}{3}\right)$$

Do the multiplications in 5\times 3-2r.

$$\frac{15-2r}{6}\left(\frac{5}{2}+\frac{r}{3}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{5}{2} times \frac{3}{3}. Multiply \frac{r}{3} times \frac{2}{2}.

$$\frac{15-2r}{6}\left(\frac{5\times 3}{6}+\frac{2r}{6}\right)$$

Since \frac{5\times 3}{6} and \frac{2r}{6} have the same denominator, add them by adding their numerators.

$$\frac{15-2r}{6}\times \frac{5\times 3+2r}{6}$$

Do the multiplications in 5\times 3+2r.

$$\frac{15-2r}{6}\times \frac{15+2r}{6}$$

Multiply \frac{15-2r}{6} times \frac{15+2r}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(15-2r\right)\left(15+2r\right)}{6\times 6}$$

Multiply 6 and 6 to get 36.

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

Consider \left(15-2r\right)\left(15+2r\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Calculate 15 to the power of 2 and get 225.

$$\frac{225-\left(2r\right)^{2}}{36}$$

Expand \left(2r\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{5}{2} times \frac{3}{3}. Multiply \frac{r}{3} times \frac{2}{2}.

$$\left(\frac{5\times 3}{6}-\frac{2r}{6}\right)\left(\frac{5}{2}+\frac{r}{3}\right)$$

Since \frac{5\times 3}{6} and \frac{2r}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\times 3-2r}{6}\left(\frac{5}{2}+\frac{r}{3}\right)$$

Do the multiplications in 5\times 3-2r.

$$\frac{15-2r}{6}\left(\frac{5}{2}+\frac{r}{3}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{5}{2} times \frac{3}{3}. Multiply \frac{r}{3} times \frac{2}{2}.

$$\frac{15-2r}{6}\left(\frac{5\times 3}{6}+\frac{2r}{6}\right)$$

Since \frac{5\times 3}{6} and \frac{2r}{6} have the same denominator, add them by adding their numerators.

$$\frac{15-2r}{6}\times \frac{5\times 3+2r}{6}$$

Do the multiplications in 5\times 3+2r.

$$\frac{15-2r}{6}\times \frac{15+2r}{6}$$

Multiply \frac{15-2r}{6} times \frac{15+2r}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(15-2r\right)\left(15+2r\right)}{6\times 6}$$

Multiply 6 and 6 to get 36.

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

Consider \left(15-2r\right)\left(15+2r\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Calculate 15 to the power of 2 and get 225.

$$\frac{225-\left(2r\right)^{2}}{36}$$

Expand \left(2r\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

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