Find the Perfect Square Trinomial n^2+(2n)/3

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

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

Multiply the numerator by the reciprocal of the denominator.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the expression.

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

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

One to any power is one.

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

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

$\frac{1}{9}$

Add $\frac{1}{9}$ to get the perfect square trinomial.

$n^{2} + \frac{2 n}{3} + \frac{1}{9}$