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

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

Step 1

Factor out the $9$

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

Step 2

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

Multiply the numerator by the reciprocal of the denominator.

${(\frac{4}{3} \cdot \frac{1}{2})}^{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

${(\frac{2 (2)}{3} \cdot \frac{1}{2})}^{2}$

Cancel the common factor.

${(\frac{2 \cdot 2}{3} \cdot \frac{1}{2})}^{2}$

Rewrite the expression.

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

Simplify the expression.

Apply the product rule to $\frac{2}{3}$ .

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

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

$\frac{4}{3^{2}}$

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

$\frac{4}{9}$

Step 3

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

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

Step 4

Simplify.

Combine the numerators over the common denominator.

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

Add $4$ and $4$ .

$9 (x^{2} + \frac{4 x}{3} + \frac{8}{9})$

Apply the distributive property.

$9 x^{2} + 9 \frac{4 x}{3} + 9 (\frac{8}{9})$

Simplify.

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$9 x^{2} + 3 (3) \frac{4 x}{3} + 9 (\frac{8}{9})$

Cancel the common factor.

$9 x^{2} + 3 \cdot 3 \frac{4 x}{3} + 9 (\frac{8}{9})$

Rewrite the expression.

$9 x^{2} + 3 (4 x) + 9 (\frac{8}{9})$

Multiply $4$ by $3$ .

$9 x^{2} + 12 x + 9 (\frac{8}{9})$

Cancel the common factor of $9$ .

Cancel the common factor.

$9 x^{2} + 12 x + 9 (\frac{8}{9})$

Rewrite the expression.

$9 x^{2} + 12 x + 8$

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

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