Solve =(5x/2-1/3)(2x+4)-(5x/2-1/3)(6-5x)

$$= ( \frac { 5 x } { 2 } - \frac { 1 } { 3 } ) ( 2 x + 4 ) - ( \frac { 5 x } { 2 } - \frac { 1 } { 3 } ) ( 6 - 5 x )$$

Evaluate

$$\frac{35x^{2}}{2}-\frac{22x}{3}+\frac{2}{3}$$

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{5x}{2} times \frac{3}{3}. Multiply \frac{1}{3} times \frac{2}{2}.

$$\left(\frac{3\times 5x}{6}-\frac{2}{6}\right)\left(2x+4\right)-\left(\frac{5x}{2}-\frac{1}{3}\right)\left(6-5x\right)$$

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

$$\frac{3\times 5x-2}{6}\left(2x+4\right)-\left(\frac{5x}{2}-\frac{1}{3}\right)\left(6-5x\right)$$

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

$$\frac{15x-2}{6}\left(2x+4\right)-\left(\frac{5x}{2}-\frac{1}{3}\right)\left(6-5x\right)$$

Express \frac{15x-2}{6}\left(2x+4\right) as a single fraction.

$$\frac{\left(15x-2\right)\left(2x+4\right)}{6}-\left(\frac{5x}{2}-\frac{1}{3}\right)\left(6-5x\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{5x}{2} times \frac{3}{3}. Multiply \frac{1}{3} times \frac{2}{2}.

$$\frac{\left(15x-2\right)\left(2x+4\right)}{6}-\left(\frac{3\times 5x}{6}-\frac{2}{6}\right)\left(6-5x\right)$$

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

$$\frac{\left(15x-2\right)\left(2x+4\right)}{6}-\frac{3\times 5x-2}{6}\left(6-5x\right)$$

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

$$\frac{\left(15x-2\right)\left(2x+4\right)}{6}-\frac{15x-2}{6}\left(6-5x\right)$$

Express \frac{15x-2}{6}\left(6-5x\right) as a single fraction.

$$\frac{\left(15x-2\right)\left(2x+4\right)}{6}-\frac{\left(15x-2\right)\left(6-5x\right)}{6}$$

Since \frac{\left(15x-2\right)\left(2x+4\right)}{6} and \frac{\left(15x-2\right)\left(6-5x\right)}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(15x-2\right)\left(2x+4\right)-\left(15x-2\right)\left(6-5x\right)}{6}$$

Do the multiplications in \left(15x-2\right)\left(2x+4\right)-\left(15x-2\right)\left(6-5x\right).

$$\frac{30x^{2}+60x-4x-8-90x+75x^{2}+12-10x}{6}$$

Combine like terms in 30x^{2}+60x-4x-8-90x+75x^{2}+12-10x.

$$\frac{105x^{2}-44x+4}{6}$$

Expand

$$\frac{35x^{2}}{2}-\frac{22x}{3}+\frac{2}{3}$$

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{5x}{2} times \frac{3}{3}. Multiply \frac{1}{3} times \frac{2}{2}.

$$\left(\frac{3\times 5x}{6}-\frac{2}{6}\right)\left(2x+4\right)-\left(\frac{5x}{2}-\frac{1}{3}\right)\left(6-5x\right)$$

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

$$\frac{3\times 5x-2}{6}\left(2x+4\right)-\left(\frac{5x}{2}-\frac{1}{3}\right)\left(6-5x\right)$$

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

$$\frac{15x-2}{6}\left(2x+4\right)-\left(\frac{5x}{2}-\frac{1}{3}\right)\left(6-5x\right)$$

Express \frac{15x-2}{6}\left(2x+4\right) as a single fraction.

$$\frac{\left(15x-2\right)\left(2x+4\right)}{6}-\left(\frac{5x}{2}-\frac{1}{3}\right)\left(6-5x\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{5x}{2} times \frac{3}{3}. Multiply \frac{1}{3} times \frac{2}{2}.

$$\frac{\left(15x-2\right)\left(2x+4\right)}{6}-\left(\frac{3\times 5x}{6}-\frac{2}{6}\right)\left(6-5x\right)$$

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

$$\frac{\left(15x-2\right)\left(2x+4\right)}{6}-\frac{3\times 5x-2}{6}\left(6-5x\right)$$

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

$$\frac{\left(15x-2\right)\left(2x+4\right)}{6}-\frac{15x-2}{6}\left(6-5x\right)$$

Express \frac{15x-2}{6}\left(6-5x\right) as a single fraction.

$$\frac{\left(15x-2\right)\left(2x+4\right)}{6}-\frac{\left(15x-2\right)\left(6-5x\right)}{6}$$

Since \frac{\left(15x-2\right)\left(2x+4\right)}{6} and \frac{\left(15x-2\right)\left(6-5x\right)}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(15x-2\right)\left(2x+4\right)-\left(15x-2\right)\left(6-5x\right)}{6}$$

Do the multiplications in \left(15x-2\right)\left(2x+4\right)-\left(15x-2\right)\left(6-5x\right).

$$\frac{30x^{2}+60x-4x-8-90x+75x^{2}+12-10x}{6}$$

Combine like terms in 30x^{2}+60x-4x-8-90x+75x^{2}+12-10x.

$$\frac{105x^{2}-44x+4}{6}$$