Solve 442+((x-17)+(x-17)(x-18)/2*-3)

$$442+((x-17)+ \frac{ (x-17)(x-18) }{ 2 } \times -3)$$

Evaluate

$$-\frac{3x^{2}}{2}+\frac{107x}{2}-34$$

Short Solution Steps

Subtract 17 from 442 to get 425.

$$425+x+\frac{\left(x-17\right)\left(x-18\right)}{2}\left(-3\right)$$

Apply the distributive property by multiplying each term of x-17 by each term of x-18.

$$425+x+\frac{x^{2}-18x-17x+306}{2}\left(-3\right)$$

Combine -18x and -17x to get -35x.

$$425+x+\frac{x^{2}-35x+306}{2}\left(-3\right)$$

Express \frac{x^{2}-35x+306}{2}\left(-3\right) as a single fraction.

$$425+x+\frac{-\left(x^{2}-35x+306\right)\times 3}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 425+x times \frac{2}{2}.

$$\frac{2\left(425+x\right)}{2}+\frac{-\left(x^{2}-35x+306\right)\times 3}{2}$$

Since \frac{2\left(425+x\right)}{2} and \frac{-\left(x^{2}-35x+306\right)\times 3}{2} have the same denominator, add them by adding their numerators.

$$\frac{2\left(425+x\right)-\left(x^{2}-35x+306\right)\times 3}{2}$$

Do the multiplications in 2\left(425+x\right)-\left(x^{2}-35x+306\right)\times 3.

$$\frac{850+2x-3x^{2}+105x-918}{2}$$

Combine like terms in 850+2x-3x^{2}+105x-918.

$$\frac{-68+107x-3x^{2}}{2}$$

Expand

$$-\frac{3x^{2}}{2}+\frac{107x}{2}-34$$

Short Solution Steps

Subtract 17 from 442 to get 425.

$$425+x+\frac{\left(x-17\right)\left(x-18\right)}{2}\left(-3\right)$$

Apply the distributive property by multiplying each term of x-17 by each term of x-18.

$$425+x+\frac{x^{2}-18x-17x+306}{2}\left(-3\right)$$

Combine -18x and -17x to get -35x.

$$425+x+\frac{x^{2}-35x+306}{2}\left(-3\right)$$

Express \frac{x^{2}-35x+306}{2}\left(-3\right) as a single fraction.

$$425+x+\frac{-\left(x^{2}-35x+306\right)\times 3}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 425+x times \frac{2}{2}.

$$\frac{2\left(425+x\right)}{2}+\frac{-\left(x^{2}-35x+306\right)\times 3}{2}$$

Since \frac{2\left(425+x\right)}{2} and \frac{-\left(x^{2}-35x+306\right)\times 3}{2} have the same denominator, add them by adding their numerators.

$$\frac{2\left(425+x\right)-\left(x^{2}-35x+306\right)\times 3}{2}$$

Do the multiplications in 2\left(425+x\right)-\left(x^{2}-35x+306\right)\times 3.

$$\frac{850+2x-3x^{2}+105x-918}{2}$$

Combine like terms in 850+2x-3x^{2}+105x-918.

$$\frac{-68+107x-3x^{2}}{2}$$