Algebra Examples

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

Step 1

Combine fractions.

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Step 1.1

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

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

Step 1.2

Rewrite ${(\frac{2 x}{3} - 1)}^{2}$ as $(\frac{2 x}{3} - 1) (\frac{2 x}{3} - 1)$ .

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

Step 2

Expand $(\frac{2 x}{3} - 1) (\frac{2 x}{3} - 1)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

$\frac{2 x}{3} \cdot \frac{2 x}{3} + \frac{2 x}{3} \cdot - 1 - 1 \frac{2 x}{3} - 1 \cdot - 1$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $\frac{2 x}{3} \cdot \frac{2 x}{3}$ .

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Step 3.1.1.1

Multiply $\frac{2 x}{3}$ by $\frac{2 x}{3}$ .

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

Step 3.1.1.2

Multiply $2$ by $2$ .

$\frac{4 x \cdot x}{3 \cdot 3} + \frac{2 x}{3} \cdot - 1 - 1 \frac{2 x}{3} - 1 \cdot - 1$

Step 3.1.1.3

Raise $x$ to the power of $1$ .

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

Step 3.1.1.4

Raise $x$ to the power of $1$ .

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

Step 3.1.1.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 x^{1 + 1}}{3 \cdot 3} + \frac{2 x}{3} \cdot - 1 - 1 \frac{2 x}{3} - 1 \cdot - 1$

Step 3.1.1.6

Add $1$ and $1$ .

$\frac{4 x^{2}}{3 \cdot 3} + \frac{2 x}{3} \cdot - 1 - 1 \frac{2 x}{3} - 1 \cdot - 1$

Step 3.1.1.7

Multiply $3$ by $3$ .

$\frac{4 x^{2}}{9} + \frac{2 x}{3} \cdot - 1 - 1 \frac{2 x}{3} - 1 \cdot - 1$

Step 3.1.2

Multiply $\frac{2 x}{3} \cdot - 1$ .

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Step 3.1.2.1

Combine $\frac{2 x}{3}$ and $- 1$ .

$\frac{4 x^{2}}{9} + \frac{2 x \cdot - 1}{3} - 1 \frac{2 x}{3} - 1 \cdot - 1$

Step 3.1.2.2

Multiply $- 1$ by $2$ .

$\frac{4 x^{2}}{9} + \frac{- 2 x}{3} - 1 \frac{2 x}{3} - 1 \cdot - 1$

Step 3.1.3

Move the negative in front of the fraction.

$\frac{4 x^{2}}{9} - \frac{2 x}{3} - 1 \frac{2 x}{3} - 1 \cdot - 1$

Step 3.1.4

Rewrite $- 1 \frac{2 x}{3}$ as $- \frac{2 x}{3}$ .

$\frac{4 x^{2}}{9} - \frac{2 x}{3} - \frac{2 x}{3} - 1 \cdot - 1$

Step 3.1.5

Multiply $- 1$ by $- 1$ .

$\frac{4 x^{2}}{9} - \frac{2 x}{3} - \frac{2 x}{3} + 1$

Step 3.2

Subtract $\frac{2 x}{3}$ from $- \frac{2 x}{3}$ .

$\frac{4 x^{2}}{9} - 2 \frac{2 x}{3} + 1$

Step 4

Simplify each term.

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Step 4.1

Multiply $- 2 \frac{2 x}{3}$ .

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Step 4.1.1

Combine $- 2$ and $\frac{2 x}{3}$ .

$\frac{4 x^{2}}{9} + \frac{- 2 (2 x)}{3} + 1$

Step 4.1.2

Multiply $2$ by $- 2$ .

$\frac{4 x^{2}}{9} + \frac{- 4 x}{3} + 1$

Step 4.2

Move the negative in front of the fraction.

$\frac{4 x^{2}}{9} - \frac{4 x}{3} + 1$