Find the Perfect Square Trinomial x^2+4xy+4y^2

$x^{2} + 4 x y + 4 y^{2}$

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

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 y$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $2 y$ by $1$ .

${(2 y)}^{2}$

Simplify the expression.

Apply the product rule to $2 y$ .

$2^{2} y^{2}$

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

$4 y^{2}$

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

$x^{2} + 4 x y + 8 y^{2}$