Solve (x-0)(x-2)(x-3)/(1-9)(1-2)(1-3)

$$\frac { ( x - 0 ) ( x - 2 ) ( x - 3 ) } { ( 1 - 9 ) ( 1 - 2 ) ( 1 - 3 ) }$$

Evaluate

$$-\frac{x\left(x-3\right)\left(x-2\right)}{16}$$

Solution Steps

Subtract 9 from 1 to get -8.

$$\frac{\left(x-0\right)\left(x-2\right)\left(x-3\right)}{-8\left(1-2\right)\left(1-3\right)}$$

Subtract 2 from 1 to get -1.

$$\frac{\left(x-0\right)\left(x-2\right)\left(x-3\right)}{-8\left(-1\right)\left(1-3\right)}$$

Multiply -8 and -1 to get 8.

$$\frac{\left(x-0\right)\left(x-2\right)\left(x-3\right)}{8\left(1-3\right)}$$

Subtract 3 from 1 to get -2.

$$\frac{\left(x-0\right)\left(x-2\right)\left(x-3\right)}{8\left(-2\right)}$$

Multiply 8 and -2 to get -16.

$$\frac{\left(x-0\right)\left(x-2\right)\left(x-3\right)}{-16}$$

Use the distributive property to multiply x-0 by x-2.

$$\frac{\left(\left(x-0\right)x-2\left(x-0\right)\right)\left(x-3\right)}{-16}$$

Apply the distributive property by multiplying each term of \left(x-0\right)x-2\left(x-0\right) by each term of x-3.

$$\frac{\left(x-0\right)x^{2}-3\left(x-0\right)x-2\left(x-0\right)x+6\left(x-0\right)}{-16}$$

Combine -3\left(x-0\right)x and -2\left(x-0\right)x to get -5\left(x-0\right)x.

$$\frac{\left(x-0\right)x^{2}-5\left(x-0\right)x+6\left(x-0\right)}{-16}$$

Multiply -1 and 0 to get 0.

$$\frac{\left(x+0\right)x^{2}-5\left(x-0\right)x+6\left(x-0\right)}{-16}$$

Anything plus zero gives itself.

$$\frac{xx^{2}-5\left(x-0\right)x+6\left(x-0\right)}{-16}$$

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

$$\frac{x^{3}-5\left(x-0\right)x+6\left(x-0\right)}{-16}$$

Multiply -1 and 0 to get 0.

$$\frac{x^{3}-5xx+6\left(x-0\right)}{-16}$$

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

$$\frac{x^{3}-5x^{2}+6\left(x-0\right)}{-16}$$

Multiply -1 and 0 to get 0.

$$\frac{x^{3}-5x^{2}+6\left(x+0\right)}{-16}$$

Anything plus zero gives itself.

$$\frac{x^{3}-5x^{2}+6x}{-16}$$

Expand

$$-\frac{x^{3}}{16}+\frac{5x^{2}}{16}-\frac{3x}{8}$$

Solution Steps

Subtract 9 from 1 to get -8.

$$\frac{\left(x-0\right)\left(x-2\right)\left(x-3\right)}{-8\left(1-2\right)\left(1-3\right)}$$

Subtract 2 from 1 to get -1.

$$\frac{\left(x-0\right)\left(x-2\right)\left(x-3\right)}{-8\left(-1\right)\left(1-3\right)}$$

Multiply -8 and -1 to get 8.

$$\frac{\left(x-0\right)\left(x-2\right)\left(x-3\right)}{8\left(1-3\right)}$$

Subtract 3 from 1 to get -2.

$$\frac{\left(x-0\right)\left(x-2\right)\left(x-3\right)}{8\left(-2\right)}$$

Multiply 8 and -2 to get -16.

$$\frac{\left(x-0\right)\left(x-2\right)\left(x-3\right)}{-16}$$

Use the distributive property to multiply x-0 by x-2.

$$\frac{\left(\left(x-0\right)x-2\left(x-0\right)\right)\left(x-3\right)}{-16}$$

Apply the distributive property by multiplying each term of \left(x-0\right)x-2\left(x-0\right) by each term of x-3.

$$\frac{\left(x-0\right)x^{2}-3\left(x-0\right)x-2\left(x-0\right)x+6\left(x-0\right)}{-16}$$

Combine -3\left(x-0\right)x and -2\left(x-0\right)x to get -5\left(x-0\right)x.

$$\frac{\left(x-0\right)x^{2}-5\left(x-0\right)x+6\left(x-0\right)}{-16}$$

Multiply -1 and 0 to get 0.

$$\frac{\left(x+0\right)x^{2}-5\left(x-0\right)x+6\left(x-0\right)}{-16}$$

Anything plus zero gives itself.

$$\frac{xx^{2}-5\left(x-0\right)x+6\left(x-0\right)}{-16}$$

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

$$\frac{x^{3}-5\left(x-0\right)x+6\left(x-0\right)}{-16}$$

Multiply -1 and 0 to get 0.

$$\frac{x^{3}-5xx+6\left(x-0\right)}{-16}$$

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

$$\frac{x^{3}-5x^{2}+6\left(x-0\right)}{-16}$$

Multiply -1 and 0 to get 0.

$$\frac{x^{3}-5x^{2}+6\left(x+0\right)}{-16}$$

Anything plus zero gives itself.

$$\frac{x^{3}-5x^{2}+6x}{-16}$$