Find the Perfect Square Trinomial x^2+1/3x+

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

Step 1

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

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

Step 2

To find the $c$ value $c = {(\frac{b}{2})}^{2}$ , divide the coefficient of $x$ by $2$ and square the result.

Multiply the numerator by the reciprocal of the denominator.

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

Multiply $\frac{1}{3} \cdot \frac{1}{2}$ .

Multiply $\frac{1}{3}$ by $\frac{1}{2}$ .

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

Multiply $3$ by $2$ .

${(\frac{1}{6})}^{2}$

Apply the product rule to $\frac{1}{6}$ .

$\frac{1^{2}}{6^{2}}$

One to any power is one.

$\frac{1}{6^{2}}$

Raise $6$ to the power of $2$ .

$\frac{1}{36}$

Step 3

Add $\frac{1}{36}$ to get the perfect square trinomial.

$x^{2} + \frac{1}{3} x + \frac{1}{36}$