Algebra Examples

$9 x^{2} + 2 x$

Step 1

Factor out the $9$

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

Step 2

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

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Step 2.1

Multiply the numerator by the reciprocal of the denominator.

${(\frac{2}{9} \cdot \frac{1}{2})}^{2}$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Cancel the common factor.

${(\frac{2}{9} \cdot \frac{1}{2})}^{2}$

Step 2.2.2

Rewrite the expression.

${(\frac{1}{9})}^{2}$

Step 2.3

Simplify the expression.

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Step 2.3.1

Apply the product rule to $\frac{1}{9}$ .

$\frac{1^{2}}{9^{2}}$

Step 2.3.2

One to any power is one.

$\frac{1}{9^{2}}$

Step 2.3.3

Raise $9$ to the power of $2$ .

$\frac{1}{81}$

Step 3

Add $\frac{1}{81}$ to get the perfect square trinomial.

$9 (x^{2} + \frac{2 x}{9} + \frac{1}{81})$

Step 4

Simplify.

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Step 4.1

Apply the distributive property.

$9 x^{2} + 9 \frac{2 x}{9} + 9 (\frac{1}{81})$

Step 4.2

Simplify.

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Step 4.2.1

Cancel the common factor of $9$ .

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Step 4.2.1.1

Cancel the common factor.

$9 x^{2} + 9 \frac{2 x}{9} + 9 (\frac{1}{81})$

Step 4.2.1.2

Rewrite the expression.

$9 x^{2} + 2 x + 9 (\frac{1}{81})$

Step 4.2.2

Cancel the common factor of $9$ .

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Step 4.2.2.1

Factor $9$ out of $81$ .

$9 x^{2} + 2 x + 9 \frac{1}{9 (9)}$

Step 4.2.2.2

Cancel the common factor.

$9 x^{2} + 2 x + 9 \frac{1}{9 \cdot 9}$

Step 4.2.2.3

Rewrite the expression.

$9 x^{2} + 2 x + \frac{1}{9}$

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