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

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

Evaluate

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

Solution Steps

Add 1 and 1 to get 2.

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

Add 1 and 2 to get 3.

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

Use the distributive property to multiply \frac{1}{3} by x+2.

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

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

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

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

$$\frac{1}{3}xx+\frac{1}{3}x\times 3+\frac{2}{3}x+\frac{2}{3}\times 3$$

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

$$\frac{1}{3}x^{2}+\frac{1}{3}x\times 3+\frac{2}{3}x+\frac{2}{3}\times 3$$

Cancel out 3 and 3.

$$\frac{1}{3}x^{2}+x+\frac{2}{3}x+\frac{2}{3}\times 3$$

Combine x and \frac{2}{3}x to get \frac{5}{3}x.

$$\frac{1}{3}x^{2}+\frac{5}{3}x+\frac{2}{3}\times 3$$

Cancel out 3 and 3.

$$\frac{1}{3}x^{2}+\frac{5}{3}x+2$$

Expand

$$\frac{x^{2}}{3}+\frac{5x}{3}+2$$

Solution Steps

Add 1 and 1 to get 2.

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

Add 1 and 2 to get 3.

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

Use the distributive property to multiply \frac{1}{3} by x+2.

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

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

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

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

$$\frac{1}{3}xx+\frac{1}{3}x\times 3+\frac{2}{3}x+\frac{2}{3}\times 3$$

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

$$\frac{1}{3}x^{2}+\frac{1}{3}x\times 3+\frac{2}{3}x+\frac{2}{3}\times 3$$

Cancel out 3 and 3.

$$\frac{1}{3}x^{2}+x+\frac{2}{3}x+\frac{2}{3}\times 3$$

Combine x and \frac{2}{3}x to get \frac{5}{3}x.

$$\frac{1}{3}x^{2}+\frac{5}{3}x+\frac{2}{3}\times 3$$

Cancel out 3 and 3.

$$\frac{1}{3}x^{2}+\frac{5}{3}x+2$$