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

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

Evaluate

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

Solution Steps

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

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

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

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

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

$$x^{3}+2x^{2}+\frac{4}{3}xx+\frac{4}{3}x\times 2+\frac{1}{3}x+\frac{1}{3}\times 2$$

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

$$x^{3}+2x^{2}+\frac{4}{3}x^{2}+\frac{4}{3}x\times 2+\frac{1}{3}x+\frac{1}{3}\times 2$$

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

$$x^{3}+\frac{10}{3}x^{2}+\frac{4}{3}x\times 2+\frac{1}{3}x+\frac{1}{3}\times 2$$

Express \frac{4}{3}\times 2 as a single fraction.

$$x^{3}+\frac{10}{3}x^{2}+\frac{4\times 2}{3}x+\frac{1}{3}x+\frac{1}{3}\times 2$$

Multiply 4 and 2 to get 8.

$$x^{3}+\frac{10}{3}x^{2}+\frac{8}{3}x+\frac{1}{3}x+\frac{1}{3}\times 2$$

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

$$x^{3}+\frac{10}{3}x^{2}+3x+\frac{1}{3}\times 2$$

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

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

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.

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

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

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

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

$$x^{3}+2x^{2}+\frac{4}{3}xx+\frac{4}{3}x\times 2+\frac{1}{3}x+\frac{1}{3}\times 2$$

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

$$x^{3}+2x^{2}+\frac{4}{3}x^{2}+\frac{4}{3}x\times 2+\frac{1}{3}x+\frac{1}{3}\times 2$$

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

$$x^{3}+\frac{10}{3}x^{2}+\frac{4}{3}x\times 2+\frac{1}{3}x+\frac{1}{3}\times 2$$

Express \frac{4}{3}\times 2 as a single fraction.

$$x^{3}+\frac{10}{3}x^{2}+\frac{4\times 2}{3}x+\frac{1}{3}x+\frac{1}{3}\times 2$$

Multiply 4 and 2 to get 8.

$$x^{3}+\frac{10}{3}x^{2}+\frac{8}{3}x+\frac{1}{3}x+\frac{1}{3}\times 2$$

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

$$x^{3}+\frac{10}{3}x^{2}+3x+\frac{1}{3}\times 2$$

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

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