Solve 1/2left(10-x/3right)left(30-9xright)

$$\frac{ 1 }{ 2 } \left( 10- \frac{ x }{ 3 } \right) \left( 30-9x \right)$$

Evaluate

$$\frac{\left(x-30\right)\left(3x-10\right)}{2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 10 times \frac{3}{3}.

$$\frac{1}{2}\left(\frac{10\times 3}{3}-\frac{x}{3}\right)\left(30-9x\right)$$

Since \frac{10\times 3}{3} and \frac{x}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}\times \frac{10\times 3-x}{3}\left(30-9x\right)$$

Do the multiplications in 10\times 3-x.

$$\frac{1}{2}\times \frac{30-x}{3}\left(30-9x\right)$$

Multiply \frac{1}{2} times \frac{30-x}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{30-x}{2\times 3}\left(30-9x\right)$$

Express \frac{30-x}{2\times 3}\left(30-9x\right) as a single fraction.

$$\frac{\left(30-x\right)\left(30-9x\right)}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{\left(30-x\right)\left(30-9x\right)}{6}$$

Apply the distributive property by multiplying each term of 30-x by each term of 30-9x.

$$\frac{900-270x-30x+9x^{2}}{6}$$

Combine -270x and -30x to get -300x.

$$\frac{900-300x+9x^{2}}{6}$$

Expand

$$\frac{3x^{2}}{2}-50x+150$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 10 times \frac{3}{3}.

$$\frac{1}{2}\left(\frac{10\times 3}{3}-\frac{x}{3}\right)\left(30-9x\right)$$

Since \frac{10\times 3}{3} and \frac{x}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}\times \frac{10\times 3-x}{3}\left(30-9x\right)$$

Do the multiplications in 10\times 3-x.

$$\frac{1}{2}\times \frac{30-x}{3}\left(30-9x\right)$$

Multiply \frac{1}{2} times \frac{30-x}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{30-x}{2\times 3}\left(30-9x\right)$$

Express \frac{30-x}{2\times 3}\left(30-9x\right) as a single fraction.

$$\frac{\left(30-x\right)\left(30-9x\right)}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{\left(30-x\right)\left(30-9x\right)}{6}$$

Apply the distributive property by multiplying each term of 30-x by each term of 30-9x.

$$\frac{900-270x-30x+9x^{2}}{6}$$

Combine -270x and -30x to get -300x.

$$\frac{900-300x+9x^{2}}{6}$$