Find the Perfect Square Trinomial x^2+xy+y^2

$x^{2} + x y + y^{2}$

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

Apply the product rule to $\frac{y}{2}$ .

$\frac{y^{2}}{2^{2}}$

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

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

Add $\frac{y^{2}}{4}$ to get the perfect square trinomial.

To write $y^{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x^{2} + x y + y^{2} \cdot \frac{4}{4} + \frac{y^{2}}{4}$

Combine $y^{2}$ and $\frac{4}{4}$ .

$x^{2} + x y + \frac{y^{2} \cdot 4}{4} + \frac{y^{2}}{4}$

Combine the numerators over the common denominator.

$x^{2} + x y + \frac{y^{2} \cdot 4 + y^{2}}{4}$

Add $y^{2} \cdot 4$ and $y^{2}$ .

Reorder $y^{2}$ and $4$ .

$x^{2} + x y + \frac{4 \cdot y^{2} + y^{2}}{4}$

Add $4 \cdot y^{2}$ and $y^{2}$ .

$x^{2} + x y + \frac{5 \cdot y^{2}}{4}$

$x^{2} + x y + \frac{5 y^{2}}{4}$