Solve 1/6(k+1)(k+2)(k+3)

$$\frac { 1 } { 6 } ( k + 1 ) ( k + 2 ) ( k + 3 )$$

Evaluate

$$\frac{\left(k+1\right)\left(k+2\right)\left(k+3\right)}{6}$$

Solution Steps

Use the distributive property to multiply \frac{1}{6} by k+1.

$$\left(\frac{1}{6}k+\frac{1}{6}\right)\left(k+2\right)\left(k+3\right)$$

Apply the distributive property by multiplying each term of \frac{1}{6}k+\frac{1}{6} by each term of k+2.

$$\left(\frac{1}{6}kk+\frac{1}{6}k\times 2+\frac{1}{6}k+\frac{1}{6}\times 2\right)\left(k+3\right)$$

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

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

Multiply \frac{1}{6} and 2 to get \frac{2}{6}.

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

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

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

Combine \frac{1}{3}k and \frac{1}{6}k to get \frac{1}{2}k.

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

Multiply \frac{1}{6} and 2 to get \frac{2}{6}.

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

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

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

Apply the distributive property by multiplying each term of \frac{1}{6}k^{2}+\frac{1}{2}k+\frac{1}{3} by each term of k+3.

$$\frac{1}{6}k^{2}k+\frac{1}{6}k^{2}\times 3+\frac{1}{2}kk+\frac{1}{2}k\times 3+\frac{1}{3}k+\frac{1}{3}\times 3$$

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

$$\frac{1}{6}k^{3}+\frac{1}{6}k^{2}\times 3+\frac{1}{2}kk+\frac{1}{2}k\times 3+\frac{1}{3}k+\frac{1}{3}\times 3$$

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

$$\frac{1}{6}k^{3}+\frac{1}{6}k^{2}\times 3+\frac{1}{2}k^{2}+\frac{1}{2}k\times 3+\frac{1}{3}k+\frac{1}{3}\times 3$$

Multiply \frac{1}{6} and 3 to get \frac{3}{6}.

$$\frac{1}{6}k^{3}+\frac{3}{6}k^{2}+\frac{1}{2}k^{2}+\frac{1}{2}k\times 3+\frac{1}{3}k+\frac{1}{3}\times 3$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{6}k^{3}+\frac{1}{2}k^{2}+\frac{1}{2}k^{2}+\frac{1}{2}k\times 3+\frac{1}{3}k+\frac{1}{3}\times 3$$

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

$$\frac{1}{6}k^{3}+k^{2}+\frac{1}{2}k\times 3+\frac{1}{3}k+\frac{1}{3}\times 3$$

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

$$\frac{1}{6}k^{3}+k^{2}+\frac{3}{2}k+\frac{1}{3}k+\frac{1}{3}\times 3$$

Combine \frac{3}{2}k and \frac{1}{3}k to get \frac{11}{6}k.

$$\frac{1}{6}k^{3}+k^{2}+\frac{11}{6}k+\frac{1}{3}\times 3$$

Cancel out 3 and 3.

$$\frac{1}{6}k^{3}+k^{2}+\frac{11}{6}k+1$$

Expand

$$\frac{k^{3}}{6}+k^{2}+\frac{11k}{6}+1$$

Solution Steps

Use the distributive property to multiply \frac{1}{6} by k+1.

$$\left(\frac{1}{6}k+\frac{1}{6}\right)\left(k+2\right)\left(k+3\right)$$

Apply the distributive property by multiplying each term of \frac{1}{6}k+\frac{1}{6} by each term of k+2.

$$\left(\frac{1}{6}kk+\frac{1}{6}k\times 2+\frac{1}{6}k+\frac{1}{6}\times 2\right)\left(k+3\right)$$

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

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

Multiply \frac{1}{6} and 2 to get \frac{2}{6}.

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

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

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

Combine \frac{1}{3}k and \frac{1}{6}k to get \frac{1}{2}k.

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

Multiply \frac{1}{6} and 2 to get \frac{2}{6}.

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

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

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

Apply the distributive property by multiplying each term of \frac{1}{6}k^{2}+\frac{1}{2}k+\frac{1}{3} by each term of k+3.

$$\frac{1}{6}k^{2}k+\frac{1}{6}k^{2}\times 3+\frac{1}{2}kk+\frac{1}{2}k\times 3+\frac{1}{3}k+\frac{1}{3}\times 3$$

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

$$\frac{1}{6}k^{3}+\frac{1}{6}k^{2}\times 3+\frac{1}{2}kk+\frac{1}{2}k\times 3+\frac{1}{3}k+\frac{1}{3}\times 3$$

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

$$\frac{1}{6}k^{3}+\frac{1}{6}k^{2}\times 3+\frac{1}{2}k^{2}+\frac{1}{2}k\times 3+\frac{1}{3}k+\frac{1}{3}\times 3$$

Multiply \frac{1}{6} and 3 to get \frac{3}{6}.

$$\frac{1}{6}k^{3}+\frac{3}{6}k^{2}+\frac{1}{2}k^{2}+\frac{1}{2}k\times 3+\frac{1}{3}k+\frac{1}{3}\times 3$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{6}k^{3}+\frac{1}{2}k^{2}+\frac{1}{2}k^{2}+\frac{1}{2}k\times 3+\frac{1}{3}k+\frac{1}{3}\times 3$$

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

$$\frac{1}{6}k^{3}+k^{2}+\frac{1}{2}k\times 3+\frac{1}{3}k+\frac{1}{3}\times 3$$

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

$$\frac{1}{6}k^{3}+k^{2}+\frac{3}{2}k+\frac{1}{3}k+\frac{1}{3}\times 3$$

Combine \frac{3}{2}k and \frac{1}{3}k to get \frac{11}{6}k.

$$\frac{1}{6}k^{3}+k^{2}+\frac{11}{6}k+\frac{1}{3}\times 3$$

Cancel out 3 and 3.

$$\frac{1}{6}k^{3}+k^{2}+\frac{11}{6}k+1$$