Solve (x(x-1)(x-2)div2!)-x

$$(x(x-1)(x-2) \div 2 ! )-x$$

Evaluate

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

Short Solution Steps

The factorial of 2 is 2.

$$\frac{x\left(x-1\right)\left(x-2\right)}{2}-x$$

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

$$\frac{x\left(x-1\right)\left(x-2\right)}{2}-\frac{2x}{2}$$

Since \frac{x\left(x-1\right)\left(x-2\right)}{2} and \frac{2x}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\left(x-1\right)\left(x-2\right)-2x}{2}$$

Do the multiplications in x\left(x-1\right)\left(x-2\right)-2x.

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

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

$$\frac{x^{3}-3x^{2}}{2}$$

Factor

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

Solution Steps

The factorial of 2 is 2.

$$factor(\frac{x\left(x-1\right)\left(x-2\right)}{2}-x)$$

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

$$factor(\frac{x\left(x-1\right)\left(x-2\right)}{2}-\frac{2x}{2})$$

Since \frac{x\left(x-1\right)\left(x-2\right)}{2} and \frac{2x}{2} have the same denominator, subtract them by subtracting their numerators.

$$factor(\frac{x\left(x-1\right)\left(x-2\right)-2x}{2})$$

Do the multiplications in x\left(x-1\right)\left(x-2\right)-2x.

$$factor(\frac{x^{3}-2x^{2}-x^{2}+2x-2x}{2})$$

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

$$factor(\frac{x^{3}-3x^{2}}{2})$$

Consider x^{3}-3x^{2}. Factor out x^{2}.

$$x^{2}\left(x-3\right)$$

Rewrite the complete factored expression.

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