Algebra Examples

$m^{2} + \frac{2}{9} m + n$

Step 1

Combine $\frac{2}{9}$ and $m$ .

$m^{2} + \frac{2 m}{9} + n$

Step 2

Move $\frac{2 m}{9}$ .

$m^{2} + n + \frac{2 m}{9}$

Step 3

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

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Rewrite the expression.

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

Step 3.3

Simplify the expression.

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Step 3.3.1

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

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

Step 3.3.2

One to any power is one.

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

Step 3.3.3

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

$\frac{1}{81}$

Step 4

Combine $\frac{2}{9}$ and $m$ .

$m^{2} + \frac{2 m}{9} + n + \frac{1}{81}$