Solve -left(x-3right)left(x-2right)left(x-1right)/6*-1

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

Evaluate

$$\frac{\left(x-3\right)\left(x-2\right)\left(x-1\right)}{6}$$

Solution Steps

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

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

Combine -2x and -3x to get -5x.

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

Apply the distributive property by multiplying each term of x^{2}-5x+6 by each term of x-1.

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

Combine -x^{2} and -5x^{2} to get -6x^{2}.

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

Combine 5x and 6x to get 11x.

$$\left(-\frac{x^{3}-6x^{2}+11x-6}{6}\right)\left(-1\right)$$

Multiply -1 and -1 to get 1.

$$\frac{x^{3}-6x^{2}+11x-6}{6}$$

Expand

$$\frac{x^{3}}{6}-x^{2}+\frac{11x}{6}-1$$

Solution Steps

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

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

Combine -2x and -3x to get -5x.

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

Apply the distributive property by multiplying each term of x^{2}-5x+6 by each term of x-1.

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

Combine -x^{2} and -5x^{2} to get -6x^{2}.

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

Combine 5x and 6x to get 11x.

$$\left(-\frac{x^{3}-6x^{2}+11x-6}{6}\right)\left(-1\right)$$

Multiply -1 and -1 to get 1.

$$\frac{x^{3}-6x^{2}+11x-6}{6}$$