Find the Product (x+1/3)^4

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

Step 1

Use the Binomial Theorem.

$x^{4} + 4 x^{3} \frac{1}{3} + 6 x^{2} {(\frac{1}{3})}^{2} + 4 x {(\frac{1}{3})}^{3} + {(\frac{1}{3})}^{4}$

Step 2

Simplify each term.

Multiply $4 x^{3} \frac{1}{3}$ .

Combine $4$ and $\frac{1}{3}$ .

$x^{4} + x^{3} \frac{4}{3} + 6 x^{2} {(\frac{1}{3})}^{2} + 4 x {(\frac{1}{3})}^{3} + {(\frac{1}{3})}^{4}$

Combine $x^{3}$ and $\frac{4}{3}$ .

$x^{4} + \frac{x^{3} \cdot 4}{3} + 6 x^{2} {(\frac{1}{3})}^{2} + 4 x {(\frac{1}{3})}^{3} + {(\frac{1}{3})}^{4}$

Move $4$ to the left of $x^{3}$ .

$x^{4} + \frac{4 \cdot x^{3}}{3} + 6 x^{2} {(\frac{1}{3})}^{2} + 4 x {(\frac{1}{3})}^{3} + {(\frac{1}{3})}^{4}$

Apply the product rule to $\frac{1}{3}$ .

$x^{4} + \frac{4 x^{3}}{3} + 6 x^{2} \frac{1^{2}}{3^{2}} + 4 x {(\frac{1}{3})}^{3} + {(\frac{1}{3})}^{4}$

One to any power is one.

$x^{4} + \frac{4 x^{3}}{3} + 6 x^{2} \frac{1}{3^{2}} + 4 x {(\frac{1}{3})}^{3} + {(\frac{1}{3})}^{4}$

Raise $3$ to the power of $2$ .

$x^{4} + \frac{4 x^{3}}{3} + 6 x^{2} \frac{1}{9} + 4 x {(\frac{1}{3})}^{3} + {(\frac{1}{3})}^{4}$

Cancel the common factor of $3$ .

Factor $3$ out of $6 x^{2}$ .

$x^{4} + \frac{4 x^{3}}{3} + 3 (2 x^{2}) \frac{1}{9} + 4 x {(\frac{1}{3})}^{3} + {(\frac{1}{3})}^{4}$

Factor $3$ out of $9$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Combine $2$ and $\frac{1}{3}$ .

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

Combine $x^{2}$ and $\frac{2}{3}$ .

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

Move $2$ to the left of $x^{2}$ .

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

Apply the product rule to $\frac{1}{3}$ .

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

One to any power is one.

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

Raise $3$ to the power of $3$ .

$x^{4} + \frac{4 x^{3}}{3} + \frac{2 x^{2}}{3} + 4 x \frac{1}{27} + {(\frac{1}{3})}^{4}$

Multiply $4 x \frac{1}{27}$ .

Combine $4$ and $\frac{1}{27}$ .

$x^{4} + \frac{4 x^{3}}{3} + \frac{2 x^{2}}{3} + x \frac{4}{27} + {(\frac{1}{3})}^{4}$

Combine $x$ and $\frac{4}{27}$ .

$x^{4} + \frac{4 x^{3}}{3} + \frac{2 x^{2}}{3} + \frac{x \cdot 4}{27} + {(\frac{1}{3})}^{4}$

Move $4$ to the left of $x$ .

$x^{4} + \frac{4 x^{3}}{3} + \frac{2 x^{2}}{3} + \frac{4 \cdot x}{27} + {(\frac{1}{3})}^{4}$

Apply the product rule to $\frac{1}{3}$ .

$x^{4} + \frac{4 x^{3}}{3} + \frac{2 x^{2}}{3} + \frac{4 x}{27} + \frac{1^{4}}{3^{4}}$

One to any power is one.

$x^{4} + \frac{4 x^{3}}{3} + \frac{2 x^{2}}{3} + \frac{4 x}{27} + \frac{1}{3^{4}}$

Raise $3$ to the power of $4$ .

$x^{4} + \frac{4 x^{3}}{3} + \frac{2 x^{2}}{3} + \frac{4 x}{27} + \frac{1}{81}$

Find the Product (x+1/3)^4

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