Solve (x/2+y/3)(x/5-y/3)=

$$( x / 2 + y / 3 ) ( x / 5 - y / 3 ) =$$

Evaluate

$$\frac{\left(3x-5y\right)\left(3x+2y\right)}{90}$$

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{x}{2} times \frac{3}{3}. Multiply \frac{y}{3} times \frac{2}{2}.

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 3 is 15. Multiply \frac{x}{5} times \frac{3}{3}. Multiply \frac{y}{3} times \frac{5}{5}.

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

Since \frac{3x}{15} and \frac{5y}{15} have the same denominator, subtract them by subtracting their numerators.

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

Multiply \frac{3x+2y}{6} times \frac{3x-5y}{15} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 6 and 15 to get 90.

$$\frac{\left(3x+2y\right)\left(3x-5y\right)}{90}$$

Apply the distributive property by multiplying each term of 3x+2y by each term of 3x-5y.

$$\frac{9x^{2}-15xy+6yx-10y^{2}}{90}$$

Combine -15xy and 6yx to get -9xy.

$$\frac{9x^{2}-9xy-10y^{2}}{90}$$

Expand

$$-\frac{xy}{10}+\frac{x^{2}}{10}-\frac{y^{2}}{9}$$

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{x}{2} times \frac{3}{3}. Multiply \frac{y}{3} times \frac{2}{2}.

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 3 is 15. Multiply \frac{x}{5} times \frac{3}{3}. Multiply \frac{y}{3} times \frac{5}{5}.

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

Since \frac{3x}{15} and \frac{5y}{15} have the same denominator, subtract them by subtracting their numerators.

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

Multiply \frac{3x+2y}{6} times \frac{3x-5y}{15} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 6 and 15 to get 90.

$$\frac{\left(3x+2y\right)\left(3x-5y\right)}{90}$$

Apply the distributive property by multiplying each term of 3x+2y by each term of 3x-5y.

$$\frac{9x^{2}-15xy+6yx-10y^{2}}{90}$$

Combine -15xy and 6yx to get -9xy.

$$\frac{9x^{2}-9xy-10y^{2}}{90}$$