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

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2} times \frac{3}{3}.

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

Since \frac{x^{3}}{3} and \frac{3x^{2}}{3} have the same denominator, add them by adding their numerators.

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

Since \frac{x^{3}+3x^{2}}{3} and \frac{\left(x-1\right)^{3}}{3} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x^{3}+3x^{2}-\left(x-1\right)^{3}.

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

Combine like terms in x^{3}+3x^{2}-x^{3}+3x^{2}-3x+1.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply \left(x-1\right)^{2} times \frac{3}{3}.

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

Since \frac{6x^{2}-3x+1}{3} and \frac{3\left(x-1\right)^{2}}{3} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 6x^{2}-3x+1-3\left(x-1\right)^{2}.

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

Combine like terms in 6x^{2}-3x+1-3x^{2}+6x-3.

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

Divide each term of 3x^{2}+3x-2 by 3 to get -\frac{2}{3}+x+x^{2}.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2} times \frac{3}{3}.

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

Since \frac{x^{3}}{3} and \frac{3x^{2}}{3} have the same denominator, add them by adding their numerators.

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

Since \frac{x^{3}+3x^{2}}{3} and \frac{\left(x-1\right)^{3}}{3} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x^{3}+3x^{2}-\left(x-1\right)^{3}.

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

Combine like terms in x^{3}+3x^{2}-x^{3}+3x^{2}-3x+1.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply \left(x-1\right)^{2} times \frac{3}{3}.

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

Since \frac{6x^{2}-3x+1}{3} and \frac{3\left(x-1\right)^{2}}{3} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 6x^{2}-3x+1-3\left(x-1\right)^{2}.

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

Combine like terms in 6x^{2}-3x+1-3x^{2}+6x-3.

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

Divide each term of 3x^{2}+3x-2 by 3 to get -\frac{2}{3}+x+x^{2}.

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