Find the Perfect Square Trinomial 4x^2+12x+9

$4 x^{2} + 12 x + 9$

Step 1

Factor out the $4$

$4 (x^{2} + 3 x + \frac{9}{4})$

Step 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 $\frac{3}{2}$ .

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

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

$\frac{9}{2^{2}}$

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

$\frac{9}{4}$

Step 3

Add $\frac{9}{4}$ to get the perfect square trinomial.

$4 (x^{2} + 3 x + \frac{9}{4} + \frac{9}{4})$

Step 4

Simplify.

Combine the numerators over the common denominator.

$4 (x^{2} + 3 x + \frac{9 + 9}{4})$

Add $9$ and $9$ .

$4 (x^{2} + 3 x + \frac{18}{4})$

Cancel the common factor of $18$ and $4$ .

Factor $2$ out of $18$ .

$4 (x^{2} + 3 x + \frac{2 (9)}{4})$

Cancel the common factors.

Factor $2$ out of $4$ .

$4 (x^{2} + 3 x + \frac{2 \cdot 9}{2 \cdot 2})$

Cancel the common factor.

$4 (x^{2} + 3 x + \frac{2 \cdot 9}{2 \cdot 2})$

Rewrite the expression.

$4 (x^{2} + 3 x + \frac{9}{2})$

Apply the distributive property.

$4 x^{2} + 4 (3 x) + 4 (\frac{9}{2})$

Simplify.

Multiply $3$ by $4$ .

$4 x^{2} + 12 x + 4 (\frac{9}{2})$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$4 x^{2} + 12 x + 2 (2) \frac{9}{2}$

Cancel the common factor.

$4 x^{2} + 12 x + 2 \cdot 2 \frac{9}{2}$

Rewrite the expression.

$4 x^{2} + 12 x + 2 \cdot 9$

Multiply $2$ by $9$ .

$4 x^{2} + 12 x + 18$