Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Combine $m$ and $\frac{2}{3}$ .

$m^{2} - \frac{m \cdot 2}{3}$

Step 1.2

Move $2$ to the left of $m$ .

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

Step 2

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 2.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

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

Step 2.2.2

Factor $2$ out of $- 2$ .

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

Step 2.2.3

Cancel the common factor.

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

Step 2.2.4

Rewrite the expression.

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

Step 2.3

Move the negative in front of the fraction.

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

Step 2.4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.4.1

Apply the product rule to $- \frac{1}{3}$ .

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

Step 2.4.2

Apply the product rule to $\frac{1}{3}$ .

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

Step 2.5

Raise $- 1$ to the power of $2$ .

$1 \frac{1^{2}}{3^{2}}$

Step 2.6

Multiply $\frac{1^{2}}{3^{2}}$ by $1$ .

$\frac{1^{2}}{3^{2}}$

Step 2.7

One to any power is one.

$\frac{1}{3^{2}}$

Step 2.8

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

$\frac{1}{9}$

Step 3

Add $\frac{1}{9}$ to get the perfect square trinomial.

$m^{2} - \frac{2}{3} m + \frac{1}{9}$