Solve left(x-0right)left(x-1right)left(x-2right)/left(3-0right)left(3-1right)left(3-2right)

$$\frac{ \left( x-0 \right) \left( x-1 \right) \left( x-2 \right) }{ \left( 3-0 \right) \left( 3-1 \right) \left( 3-2 \right) }$$

Evaluate

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

Solution Steps

Subtract 0 from 3 to get 3.

$$\frac{\left(x-0\right)\left(x-1\right)\left(x-2\right)}{3\left(3-1\right)\left(3-2\right)}$$

Subtract 1 from 3 to get 2.

$$\frac{\left(x-0\right)\left(x-1\right)\left(x-2\right)}{3\times 2\left(3-2\right)}$$

Multiply 3 and 2 to get 6.

$$\frac{\left(x-0\right)\left(x-1\right)\left(x-2\right)}{6\left(3-2\right)}$$

Subtract 2 from 3 to get 1.

$$\frac{\left(x-0\right)\left(x-1\right)\left(x-2\right)}{6\times 1}$$

Multiply 6 and 1 to get 6.

$$\frac{\left(x-0\right)\left(x-1\right)\left(x-2\right)}{6}$$

Use the distributive property to multiply x-0 by x-1.

$$\frac{\left(\left(x-0\right)x-\left(x-0\right)\right)\left(x-2\right)}{6}$$

Apply the distributive property by multiplying each term of \left(x-0\right)x-\left(x-0\right) by each term of x-2.

$$\frac{\left(x-0\right)x^{2}-2\left(x-0\right)x-\left(x-0\right)x+2\left(x-0\right)}{6}$$

Combine -2\left(x-0\right)x and -\left(x-0\right)x to get -3\left(x-0\right)x.

$$\frac{\left(x-0\right)x^{2}-3\left(x-0\right)x+2\left(x-0\right)}{6}$$

Multiply -1 and 0 to get 0.

$$\frac{\left(x+0\right)x^{2}-3\left(x-0\right)x+2\left(x-0\right)}{6}$$

Anything plus zero gives itself.

$$\frac{xx^{2}-3\left(x-0\right)x+2\left(x-0\right)}{6}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{x^{3}-3\left(x-0\right)x+2\left(x-0\right)}{6}$$

Multiply -1 and 0 to get 0.

$$\frac{x^{3}-3xx+2\left(x-0\right)}{6}$$

Multiply x and x to get x^{2}.

$$\frac{x^{3}-3x^{2}+2\left(x-0\right)}{6}$$

Multiply -1 and 0 to get 0.

$$\frac{x^{3}-3x^{2}+2\left(x+0\right)}{6}$$

Anything plus zero gives itself.

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

Expand

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

Solution Steps

Subtract 0 from 3 to get 3.

$$\frac{\left(x-0\right)\left(x-1\right)\left(x-2\right)}{3\left(3-1\right)\left(3-2\right)}$$

Subtract 1 from 3 to get 2.

$$\frac{\left(x-0\right)\left(x-1\right)\left(x-2\right)}{3\times 2\left(3-2\right)}$$

Multiply 3 and 2 to get 6.

$$\frac{\left(x-0\right)\left(x-1\right)\left(x-2\right)}{6\left(3-2\right)}$$

Subtract 2 from 3 to get 1.

$$\frac{\left(x-0\right)\left(x-1\right)\left(x-2\right)}{6\times 1}$$

Multiply 6 and 1 to get 6.

$$\frac{\left(x-0\right)\left(x-1\right)\left(x-2\right)}{6}$$

Use the distributive property to multiply x-0 by x-1.

$$\frac{\left(\left(x-0\right)x-\left(x-0\right)\right)\left(x-2\right)}{6}$$

Apply the distributive property by multiplying each term of \left(x-0\right)x-\left(x-0\right) by each term of x-2.

$$\frac{\left(x-0\right)x^{2}-2\left(x-0\right)x-\left(x-0\right)x+2\left(x-0\right)}{6}$$

Combine -2\left(x-0\right)x and -\left(x-0\right)x to get -3\left(x-0\right)x.

$$\frac{\left(x-0\right)x^{2}-3\left(x-0\right)x+2\left(x-0\right)}{6}$$

Multiply -1 and 0 to get 0.

$$\frac{\left(x+0\right)x^{2}-3\left(x-0\right)x+2\left(x-0\right)}{6}$$

Anything plus zero gives itself.

$$\frac{xx^{2}-3\left(x-0\right)x+2\left(x-0\right)}{6}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{x^{3}-3\left(x-0\right)x+2\left(x-0\right)}{6}$$

Multiply -1 and 0 to get 0.

$$\frac{x^{3}-3xx+2\left(x-0\right)}{6}$$

Multiply x and x to get x^{2}.

$$\frac{x^{3}-3x^{2}+2\left(x-0\right)}{6}$$

Multiply -1 and 0 to get 0.

$$\frac{x^{3}-3x^{2}+2\left(x+0\right)}{6}$$

Anything plus zero gives itself.

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