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

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

Step 1

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

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

Step 2

Move $\frac{2 x}{3}$ .

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

Step 3

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.

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

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 $2$ .

$\frac{1}{9}$

Step 4

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

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