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

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

Evaluate

$$\frac{x^{3}}{3}-\frac{x^{2}}{2}+x+\frac{11}{6}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{\left(x+1\right)^{3}}{3} times \frac{2}{2}. Multiply \frac{3\left(x+1\right)^{2}}{2} times \frac{3}{3}.

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

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

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

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

$$\frac{2x^{3}+6x^{2}+6x+2-9x^{2}-18x-9}{6}+3\left(x+1\right)$$

Combine like terms in 2x^{3}+6x^{2}+6x+2-9x^{2}-18x-9.

$$\frac{2x^{3}-3x^{2}-12x-7}{6}+3\left(x+1\right)$$

Use the distributive property to multiply 3 by x+1.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{\left(x+1\right)^{3}}{3} times \frac{2}{2}. Multiply \frac{3\left(x+1\right)^{2}}{2} times \frac{3}{3}.

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

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

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

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

$$\frac{2x^{3}+6x^{2}+6x+2-9x^{2}-18x-9}{6}+3x+3$$

Combine like terms in 2x^{3}+6x^{2}+6x+2-9x^{2}-18x-9.

$$\frac{2x^{3}-3x^{2}-12x-7}{6}+3x+3$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x+3 times \frac{6}{6}.

$$\frac{2x^{3}-3x^{2}-12x-7}{6}+\frac{6\left(3x+3\right)}{6}$$

Since \frac{2x^{3}-3x^{2}-12x-7}{6} and \frac{6\left(3x+3\right)}{6} have the same denominator, add them by adding their numerators.

$$\frac{2x^{3}-3x^{2}-12x-7+6\left(3x+3\right)}{6}$$

Do the multiplications in 2x^{3}-3x^{2}-12x-7+6\left(3x+3\right).

$$\frac{2x^{3}-3x^{2}-12x-7+18x+18}{6}$$

Combine like terms in 2x^{3}-3x^{2}-12x-7+18x+18.

$$\frac{2x^{3}-3x^{2}+6x+11}{6}$$

Expand

$$\frac{x^{3}}{3}-\frac{x^{2}}{2}+x+\frac{11}{6}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{\left(x+1\right)^{3}}{3} times \frac{2}{2}. Multiply \frac{3\left(x+1\right)^{2}}{2} times \frac{3}{3}.

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

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

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

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

$$\frac{2x^{3}+6x^{2}+6x+2-9x^{2}-18x-9}{6}+3\left(x+1\right)$$

Combine like terms in 2x^{3}+6x^{2}+6x+2-9x^{2}-18x-9.

$$\frac{2x^{3}-3x^{2}-12x-7}{6}+3\left(x+1\right)$$

Use the distributive property to multiply 3 by x+1.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{\left(x+1\right)^{3}}{3} times \frac{2}{2}. Multiply \frac{3\left(x+1\right)^{2}}{2} times \frac{3}{3}.

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

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

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

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

$$\frac{2x^{3}+6x^{2}+6x+2-9x^{2}-18x-9}{6}+3x+3$$

Combine like terms in 2x^{3}+6x^{2}+6x+2-9x^{2}-18x-9.

$$\frac{2x^{3}-3x^{2}-12x-7}{6}+3x+3$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x+3 times \frac{6}{6}.

$$\frac{2x^{3}-3x^{2}-12x-7}{6}+\frac{6\left(3x+3\right)}{6}$$

Since \frac{2x^{3}-3x^{2}-12x-7}{6} and \frac{6\left(3x+3\right)}{6} have the same denominator, add them by adding their numerators.

$$\frac{2x^{3}-3x^{2}-12x-7+6\left(3x+3\right)}{6}$$

Do the multiplications in 2x^{3}-3x^{2}-12x-7+6\left(3x+3\right).

$$\frac{2x^{3}-3x^{2}-12x-7+18x+18}{6}$$

Combine like terms in 2x^{3}-3x^{2}-12x-7+18x+18.

$$\frac{2x^{3}-3x^{2}+6x+11}{6}$$