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

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

Step 1

Factor out the $2$

$2 (x^{2} + 4 x)$

Step 2

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

Divide $4$ by $2$ .

$2^{2}$

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

$4$

Step 3

Add $4$ to get the perfect square trinomial.

$2 (x^{2} + 4 x + 4)$

Step 4

Simplify.

Apply the distributive property.

$2 x^{2} + 2 (4 x) + 2 \cdot 4$

Simplify.

Multiply $4$ by $2$ .

$2 x^{2} + 8 x + 2 \cdot 4$

Multiply $2$ by $4$ .

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