Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

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 $1$ by $1$ .

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

Step 3.1.2

Multiply $- \frac{x}{3}$ by $1$ .

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

Step 3.1.3

Multiply $- 1$ by $1$ .

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

Step 3.1.4

Multiply $- \frac{x}{3} (- \frac{x}{3})$ .

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Step 3.1.4.1

Multiply $- 1$ by $- 1$ .

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

Step 3.1.4.2

Multiply $\frac{x}{3}$ by $1$ .

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

Step 3.1.4.3

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

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

Step 3.1.4.4

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

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

Step 3.1.4.5

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

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

Step 3.1.4.6

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

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

Step 3.1.4.7

Add $1$ and $1$ .

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

Step 3.1.4.8

Multiply $3$ by $3$ .

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

Step 3.2

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

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

Step 4

Simplify each term.

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Step 4.1

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

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

Step 4.2

Move the negative in front of the fraction.

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