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

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

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of x-\frac{1}{3} by each term of x-1.

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

Combine -x and -\frac{1}{3}x to get -\frac{4}{3}x.

$$\left(x^{2}-\frac{4}{3}x-\frac{1}{3}\left(-1\right)\right)\left(x-2\right)$$

Multiply -\frac{1}{3} and -1 to get \frac{1}{3}.

$$\left(x^{2}-\frac{4}{3}x+\frac{1}{3}\right)\left(x-2\right)$$

Apply the distributive property by multiplying each term of x^{2}-\frac{4}{3}x+\frac{1}{3} by each term of x-2.

$$x^{3}-2x^{2}-\frac{4}{3}xx-\frac{4}{3}x\left(-2\right)+\frac{1}{3}x+\frac{1}{3}\left(-2\right)$$

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

$$x^{3}-2x^{2}-\frac{4}{3}x^{2}-\frac{4}{3}x\left(-2\right)+\frac{1}{3}x+\frac{1}{3}\left(-2\right)$$

Combine -2x^{2} and -\frac{4}{3}x^{2} to get -\frac{10}{3}x^{2}.

$$x^{3}-\frac{10}{3}x^{2}-\frac{4}{3}x\left(-2\right)+\frac{1}{3}x+\frac{1}{3}\left(-2\right)$$

Express -\frac{4}{3}\left(-2\right) as a single fraction.

$$x^{3}-\frac{10}{3}x^{2}+\frac{-4\left(-2\right)}{3}x+\frac{1}{3}x+\frac{1}{3}\left(-2\right)$$

Multiply -4 and -2 to get 8.

$$x^{3}-\frac{10}{3}x^{2}+\frac{8}{3}x+\frac{1}{3}x+\frac{1}{3}\left(-2\right)$$

Combine \frac{8}{3}x and \frac{1}{3}x to get 3x.

$$x^{3}-\frac{10}{3}x^{2}+3x+\frac{1}{3}\left(-2\right)$$

Multiply \frac{1}{3} and -2 to get \frac{-2}{3}.

$$x^{3}-\frac{10}{3}x^{2}+3x+\frac{-2}{3}$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$x^{3}-\frac{10}{3}x^{2}+3x-\frac{2}{3}$$

Expand

$$x^{3}-\frac{10x^{2}}{3}+3x-\frac{2}{3}$$

Solution Steps

Apply the distributive property by multiplying each term of x-\frac{1}{3} by each term of x-1.

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

Combine -x and -\frac{1}{3}x to get -\frac{4}{3}x.

$$\left(x^{2}-\frac{4}{3}x-\frac{1}{3}\left(-1\right)\right)\left(x-2\right)$$

Multiply -\frac{1}{3} and -1 to get \frac{1}{3}.

$$\left(x^{2}-\frac{4}{3}x+\frac{1}{3}\right)\left(x-2\right)$$

Apply the distributive property by multiplying each term of x^{2}-\frac{4}{3}x+\frac{1}{3} by each term of x-2.

$$x^{3}-2x^{2}-\frac{4}{3}xx-\frac{4}{3}x\left(-2\right)+\frac{1}{3}x+\frac{1}{3}\left(-2\right)$$

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

$$x^{3}-2x^{2}-\frac{4}{3}x^{2}-\frac{4}{3}x\left(-2\right)+\frac{1}{3}x+\frac{1}{3}\left(-2\right)$$

Combine -2x^{2} and -\frac{4}{3}x^{2} to get -\frac{10}{3}x^{2}.

$$x^{3}-\frac{10}{3}x^{2}-\frac{4}{3}x\left(-2\right)+\frac{1}{3}x+\frac{1}{3}\left(-2\right)$$

Express -\frac{4}{3}\left(-2\right) as a single fraction.

$$x^{3}-\frac{10}{3}x^{2}+\frac{-4\left(-2\right)}{3}x+\frac{1}{3}x+\frac{1}{3}\left(-2\right)$$

Multiply -4 and -2 to get 8.

$$x^{3}-\frac{10}{3}x^{2}+\frac{8}{3}x+\frac{1}{3}x+\frac{1}{3}\left(-2\right)$$

Combine \frac{8}{3}x and \frac{1}{3}x to get 3x.

$$x^{3}-\frac{10}{3}x^{2}+3x+\frac{1}{3}\left(-2\right)$$

Multiply \frac{1}{3} and -2 to get \frac{-2}{3}.

$$x^{3}-\frac{10}{3}x^{2}+3x+\frac{-2}{3}$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$x^{3}-\frac{10}{3}x^{2}+3x-\frac{2}{3}$$