Pre-Algebra Examples

${(5 x - \frac{1}{3})}^{2}$

Step 1

Rewrite ${(5 x - \frac{1}{3})}^{2}$ as $(5 x - \frac{1}{3}) (5 x - \frac{1}{3})$ .

$(5 x - \frac{1}{3}) (5 x - \frac{1}{3})$

Step 2

Expand $(5 x - \frac{1}{3}) (5 x - \frac{1}{3})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$5 x (5 x - \frac{1}{3}) - \frac{1}{3} (5 x - \frac{1}{3})$

Step 2.2

Apply the distributive property.

$5 x (5 x) + 5 x (- \frac{1}{3}) - \frac{1}{3} (5 x - \frac{1}{3})$

Step 2.3

Apply the distributive property.

$5 x (5 x) + 5 x (- \frac{1}{3}) - \frac{1}{3} (5 x) - \frac{1}{3} (- \frac{1}{3})$

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

Rewrite using the commutative property of multiplication.

$5 \cdot 5 x \cdot x + 5 x (- \frac{1}{3}) - \frac{1}{3} (5 x) - \frac{1}{3} (- \frac{1}{3})$

Step 3.1.2

Multiply $x$ by $x$ by adding the exponents.

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Step 3.1.2.1

Move $x$ .

$5 \cdot 5 (x \cdot x) + 5 x (- \frac{1}{3}) - \frac{1}{3} (5 x) - \frac{1}{3} (- \frac{1}{3})$

Step 3.1.2.2

Multiply $x$ by $x$ .

$5 \cdot 5 x^{2} + 5 x (- \frac{1}{3}) - \frac{1}{3} (5 x) - \frac{1}{3} (- \frac{1}{3})$

Step 3.1.3

Multiply $5$ by $5$ .

$25 x^{2} + 5 x (- \frac{1}{3}) - \frac{1}{3} (5 x) - \frac{1}{3} (- \frac{1}{3})$

Step 3.1.4

Multiply $5 x (- \frac{1}{3})$ .

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Step 3.1.4.1

Multiply $- 1$ by $5$ .

$25 x^{2} - 5 x \frac{1}{3} - \frac{1}{3} (5 x) - \frac{1}{3} (- \frac{1}{3})$

Step 3.1.4.2

Combine $- 5$ and $\frac{1}{3}$ .

$25 x^{2} + x \frac{- 5}{3} - \frac{1}{3} (5 x) - \frac{1}{3} (- \frac{1}{3})$

Step 3.1.4.3

Combine $x$ and $\frac{- 5}{3}$ .

$25 x^{2} + \frac{x \cdot - 5}{3} - \frac{1}{3} (5 x) - \frac{1}{3} (- \frac{1}{3})$

Step 3.1.5

Move $- 5$ to the left of $x$ .

$25 x^{2} + \frac{- 5 \cdot x}{3} - \frac{1}{3} (5 x) - \frac{1}{3} (- \frac{1}{3})$

Step 3.1.6

Move the negative in front of the fraction.

$25 x^{2} - \frac{5 \cdot x}{3} - \frac{1}{3} (5 x) - \frac{1}{3} (- \frac{1}{3})$

Step 3.1.7

Multiply $- \frac{1}{3} (5 x)$ .

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Step 3.1.7.1

Multiply $5$ by $- 1$ .

$25 x^{2} - \frac{5 x}{3} - 5 (\frac{1}{3}) x - \frac{1}{3} (- \frac{1}{3})$

Step 3.1.7.2

Combine $- 5$ and $\frac{1}{3}$ .

$25 x^{2} - \frac{5 x}{3} + \frac{- 5}{3} x - \frac{1}{3} (- \frac{1}{3})$

Step 3.1.7.3

Combine $\frac{- 5}{3}$ and $x$ .

$25 x^{2} - \frac{5 x}{3} + \frac{- 5 x}{3} - \frac{1}{3} (- \frac{1}{3})$

Step 3.1.8

Move the negative in front of the fraction.

$25 x^{2} - \frac{5 x}{3} - \frac{5 x}{3} - \frac{1}{3} (- \frac{1}{3})$

Step 3.1.9

Multiply $- \frac{1}{3} (- \frac{1}{3})$ .

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Step 3.1.9.1

Multiply $- 1$ by $- 1$ .

$25 x^{2} - \frac{5 x}{3} - \frac{5 x}{3} + 1 (\frac{1}{3}) \frac{1}{3}$

Step 3.1.9.2

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

$25 x^{2} - \frac{5 x}{3} - \frac{5 x}{3} + \frac{1}{3} \cdot \frac{1}{3}$

Step 3.1.9.3

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

$25 x^{2} - \frac{5 x}{3} - \frac{5 x}{3} + \frac{1}{3 \cdot 3}$

Step 3.1.9.4

Multiply $3$ by $3$ .

$25 x^{2} - \frac{5 x}{3} - \frac{5 x}{3} + \frac{1}{9}$

Step 3.2

Subtract $\frac{5 x}{3}$ from $- \frac{5 x}{3}$ .

$25 x^{2} - 2 \frac{5 x}{3} + \frac{1}{9}$

Step 4

Simplify each term.

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Step 4.1

Multiply $- 2 \frac{5 x}{3}$ .

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Step 4.1.1

Combine $- 2$ and $\frac{5 x}{3}$ .

$25 x^{2} + \frac{- 2 (5 x)}{3} + \frac{1}{9}$

Step 4.1.2

Multiply $5$ by $- 2$ .

$25 x^{2} + \frac{- 10 x}{3} + \frac{1}{9}$

Step 4.2

Move the negative in front of the fraction.

$25 x^{2} - \frac{10 x}{3} + \frac{1}{9}$