Find the Perfect Square Trinomial 4x^2+16x+c

$4 x^{2} + 16 x + c$

Step 1

Move $16 x$ .

$4 x^{2} + c + 16 x$

Step 2

Factor out the $4$

$4 (x^{2} + 4 x + \frac{c}{4})$

Step 3

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 4

Add $4$ to get the perfect square trinomial.

$4 (x^{2} + 4 x + \frac{c}{4} + 4)$

Step 5

Simplify.

Apply the distributive property.

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

Simplify.

Multiply $4$ by $4$ .

$4 x^{2} + 16 x + 4 \frac{c}{4} + 4 \cdot 4$

Cancel the common factor of $4$ .

Cancel the common factor.

$4 x^{2} + 16 x + 4 \frac{c}{4} + 4 \cdot 4$

Rewrite the expression.

$4 x^{2} + 16 x + c + 4 \cdot 4$

Multiply $4$ by $4$ .

$4 x^{2} + 16 x + c + 16$