Solve {l}{1/3k(k+1)(k+}{+2)}

$$\left. \begin{array} { l } { \frac { 1 } { 3 } k ( k + 1 ) ( k + } \\ { + 2 ) } \end{array} \right.$$

Evaluate

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

Solution Steps

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

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

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

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

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

$$\frac{1}{3}k^{2}k+\frac{1}{3}k^{2}\times 2+\frac{1}{3}kk+\frac{1}{3}k\times 2$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{1}{3}k^{3}+\frac{1}{3}k^{2}\times 2+\frac{1}{3}kk+\frac{1}{3}k\times 2$$

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

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

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

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

Combine \frac{2}{3}k^{2} and \frac{1}{3}k^{2} to get k^{2}.

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

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

$$\frac{1}{3}k^{3}+k^{2}+\frac{2}{3}k$$

Expand

$$\frac{k^{3}}{3}+k^{2}+\frac{2k}{3}$$

Solution Steps

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

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

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

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

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

$$\frac{1}{3}k^{2}k+\frac{1}{3}k^{2}\times 2+\frac{1}{3}kk+\frac{1}{3}k\times 2$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{1}{3}k^{3}+\frac{1}{3}k^{2}\times 2+\frac{1}{3}kk+\frac{1}{3}k\times 2$$

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

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

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

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

Combine \frac{2}{3}k^{2} and \frac{1}{3}k^{2} to get k^{2}.

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

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

$$\frac{1}{3}k^{3}+k^{2}+\frac{2}{3}k$$