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

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

Evaluate

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

Solution Steps

Subtract 0 from 2 to get 2.

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

Subtract 1 from 2 to get 1.

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

Multiply 2 and 1 to get 2.

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

Subtract 3 from 2 to get -1.

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

Multiply 2 and -1 to get -2.

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

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

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

Apply the distributive property by multiplying each term of \left(x-0\right)x-\left(x-0\right) by each term of x-3.

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

Combine -3\left(x-0\right)x and -\left(x-0\right)x to get -4\left(x-0\right)x.

$$\frac{\left(x-0\right)x^{2}-4\left(x-0\right)x+3\left(x-0\right)}{-2}$$

Multiply -1 and 0 to get 0.

$$\frac{\left(x+0\right)x^{2}-4\left(x-0\right)x+3\left(x-0\right)}{-2}$$

Anything plus zero gives itself.

$$\frac{xx^{2}-4\left(x-0\right)x+3\left(x-0\right)}{-2}$$

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

$$\frac{x^{3}-4\left(x-0\right)x+3\left(x-0\right)}{-2}$$

Multiply -1 and 0 to get 0.

$$\frac{x^{3}-4xx+3\left(x-0\right)}{-2}$$

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

$$\frac{x^{3}-4x^{2}+3\left(x-0\right)}{-2}$$

Multiply -1 and 0 to get 0.

$$\frac{x^{3}-4x^{2}+3\left(x+0\right)}{-2}$$

Anything plus zero gives itself.

$$\frac{x^{3}-4x^{2}+3x}{-2}$$

Expand

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

Solution Steps

Subtract 0 from 2 to get 2.

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

Subtract 1 from 2 to get 1.

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

Multiply 2 and 1 to get 2.

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

Subtract 3 from 2 to get -1.

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

Multiply 2 and -1 to get -2.

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

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

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

Apply the distributive property by multiplying each term of \left(x-0\right)x-\left(x-0\right) by each term of x-3.

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

Combine -3\left(x-0\right)x and -\left(x-0\right)x to get -4\left(x-0\right)x.

$$\frac{\left(x-0\right)x^{2}-4\left(x-0\right)x+3\left(x-0\right)}{-2}$$

Multiply -1 and 0 to get 0.

$$\frac{\left(x+0\right)x^{2}-4\left(x-0\right)x+3\left(x-0\right)}{-2}$$

Anything plus zero gives itself.

$$\frac{xx^{2}-4\left(x-0\right)x+3\left(x-0\right)}{-2}$$

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

$$\frac{x^{3}-4\left(x-0\right)x+3\left(x-0\right)}{-2}$$

Multiply -1 and 0 to get 0.

$$\frac{x^{3}-4xx+3\left(x-0\right)}{-2}$$

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

$$\frac{x^{3}-4x^{2}+3\left(x-0\right)}{-2}$$

Multiply -1 and 0 to get 0.

$$\frac{x^{3}-4x^{2}+3\left(x+0\right)}{-2}$$

Anything plus zero gives itself.

$$\frac{x^{3}-4x^{2}+3x}{-2}$$