Find the Perfect Square Trinomial x^2+8/3x

$x^{2} + \frac{8}{3} x$

Step 1

Combine $\frac{8}{3}$ and $x$ .

$x^{2} + \frac{8 x}{3}$

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.

${(\frac{8}{3} \cdot \frac{1}{2})}^{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

${(\frac{4}{3})}^{2}$

Simplify the expression.

Apply the product rule to $\frac{4}{3}$ .

$\frac{4^{2}}{3^{2}}$

Raise $4$ to the power of $2$ .

$\frac{16}{3^{2}}$

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

$\frac{16}{9}$

Step 3

Add $\frac{16}{9}$ to get the perfect square trinomial.

$x^{2} + \frac{8}{3} x + \frac{16}{9}$