Pre-Algebra Examples

${(\frac{4}{3} x - \frac{2}{5})}^{2}$

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Combine fractions.

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Step 1.1.1

Combine $\frac{4}{3}$ and $x$ .

${(\frac{4 x}{3} - \frac{2}{5})}^{2}$

Step 1.1.2

Rewrite ${(\frac{4 x}{3} - \frac{2}{5})}^{2}$ as $(\frac{4 x}{3} - \frac{2}{5}) (\frac{4 x}{3} - \frac{2}{5})$ .

$(\frac{4 x}{3} - \frac{2}{5}) (\frac{4 x}{3} - \frac{2}{5})$

Step 1.2

Expand $(\frac{4 x}{3} - \frac{2}{5}) (\frac{4 x}{3} - \frac{2}{5})$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$\frac{4 x}{3} (\frac{4 x}{3} - \frac{2}{5}) - \frac{2}{5} (\frac{4 x}{3} - \frac{2}{5})$

Step 1.2.2

Apply the distributive property.

$\frac{4 x}{3} \cdot \frac{4 x}{3} + \frac{4 x}{3} (- \frac{2}{5}) - \frac{2}{5} (\frac{4 x}{3} - \frac{2}{5})$

Step 1.2.3

Apply the distributive property.

$\frac{4 x}{3} \cdot \frac{4 x}{3} + \frac{4 x}{3} (- \frac{2}{5}) - \frac{2}{5} \cdot \frac{4 x}{3} - \frac{2}{5} (- \frac{2}{5})$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $\frac{4 x}{3} \cdot \frac{4 x}{3}$ .

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Step 1.3.1.1.1

Multiply $\frac{4 x}{3}$ by $\frac{4 x}{3}$ .

$\frac{4 x (4 x)}{3 \cdot 3} + \frac{4 x}{3} (- \frac{2}{5}) - \frac{2}{5} \cdot \frac{4 x}{3} - \frac{2}{5} (- \frac{2}{5})$

Step 1.3.1.1.2

Multiply $4$ by $4$ .

$\frac{16 x \cdot x}{3 \cdot 3} + \frac{4 x}{3} (- \frac{2}{5}) - \frac{2}{5} \cdot \frac{4 x}{3} - \frac{2}{5} (- \frac{2}{5})$

Step 1.3.1.1.3

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

$\frac{16 (x^{1} x)}{3 \cdot 3} + \frac{4 x}{3} (- \frac{2}{5}) - \frac{2}{5} \cdot \frac{4 x}{3} - \frac{2}{5} (- \frac{2}{5})$

Step 1.3.1.1.4

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

$\frac{16 (x^{1} x^{1})}{3 \cdot 3} + \frac{4 x}{3} (- \frac{2}{5}) - \frac{2}{5} \cdot \frac{4 x}{3} - \frac{2}{5} (- \frac{2}{5})$

Step 1.3.1.1.5

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

$\frac{16 x^{1 + 1}}{3 \cdot 3} + \frac{4 x}{3} (- \frac{2}{5}) - \frac{2}{5} \cdot \frac{4 x}{3} - \frac{2}{5} (- \frac{2}{5})$

Step 1.3.1.1.6

Add $1$ and $1$ .

$\frac{16 x^{2}}{3 \cdot 3} + \frac{4 x}{3} (- \frac{2}{5}) - \frac{2}{5} \cdot \frac{4 x}{3} - \frac{2}{5} (- \frac{2}{5})$

Step 1.3.1.1.7

Multiply $3$ by $3$ .

$\frac{16 x^{2}}{9} + \frac{4 x}{3} (- \frac{2}{5}) - \frac{2}{5} \cdot \frac{4 x}{3} - \frac{2}{5} (- \frac{2}{5})$

Step 1.3.1.2

Multiply $\frac{4 x}{3} (- \frac{2}{5})$ .

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Step 1.3.1.2.1

Multiply $\frac{4 x}{3}$ by $\frac{2}{5}$ .

$\frac{16 x^{2}}{9} - \frac{4 x \cdot 2}{3 \cdot 5} - \frac{2}{5} \cdot \frac{4 x}{3} - \frac{2}{5} (- \frac{2}{5})$

Step 1.3.1.2.2

Multiply $2$ by $4$ .

$\frac{16 x^{2}}{9} - \frac{8 x}{3 \cdot 5} - \frac{2}{5} \cdot \frac{4 x}{3} - \frac{2}{5} (- \frac{2}{5})$

Step 1.3.1.2.3

Multiply $3$ by $5$ .

$\frac{16 x^{2}}{9} - \frac{8 x}{15} - \frac{2}{5} \cdot \frac{4 x}{3} - \frac{2}{5} (- \frac{2}{5})$

Step 1.3.1.3

Multiply $- \frac{2}{5} \cdot \frac{4 x}{3}$ .

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Step 1.3.1.3.1

Multiply $\frac{4 x}{3}$ by $\frac{2}{5}$ .

$\frac{16 x^{2}}{9} - \frac{8 x}{15} - \frac{4 x \cdot 2}{3 \cdot 5} - \frac{2}{5} (- \frac{2}{5})$

Step 1.3.1.3.2

Multiply $2$ by $4$ .

$\frac{16 x^{2}}{9} - \frac{8 x}{15} - \frac{8 x}{3 \cdot 5} - \frac{2}{5} (- \frac{2}{5})$

Step 1.3.1.3.3

Multiply $3$ by $5$ .

$\frac{16 x^{2}}{9} - \frac{8 x}{15} - \frac{8 x}{15} - \frac{2}{5} (- \frac{2}{5})$

Step 1.3.1.4

Multiply $- \frac{2}{5} (- \frac{2}{5})$ .

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Step 1.3.1.4.1

Multiply $- 1$ by $- 1$ .

$\frac{16 x^{2}}{9} - \frac{8 x}{15} - \frac{8 x}{15} + 1 (\frac{2}{5}) \frac{2}{5}$

Step 1.3.1.4.2

Multiply $\frac{2}{5}$ by $1$ .

$\frac{16 x^{2}}{9} - \frac{8 x}{15} - \frac{8 x}{15} + \frac{2}{5} \cdot \frac{2}{5}$

Step 1.3.1.4.3

Multiply $\frac{2}{5}$ by $\frac{2}{5}$ .

$\frac{16 x^{2}}{9} - \frac{8 x}{15} - \frac{8 x}{15} + \frac{2 \cdot 2}{5 \cdot 5}$

Step 1.3.1.4.4

Multiply $2$ by $2$ .

$\frac{16 x^{2}}{9} - \frac{8 x}{15} - \frac{8 x}{15} + \frac{4}{5 \cdot 5}$

Step 1.3.1.4.5

Multiply $5$ by $5$ .

$\frac{16 x^{2}}{9} - \frac{8 x}{15} - \frac{8 x}{15} + \frac{4}{25}$

Step 1.3.2

Subtract $\frac{8 x}{15}$ from $- \frac{8 x}{15}$ .

$\frac{16 x^{2}}{9} - 2 \frac{8 x}{15} + \frac{4}{25}$

Step 1.4

Simplify each term.

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Step 1.4.1

Multiply $- 2 \frac{8 x}{15}$ .

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Step 1.4.1.1

Combine $- 2$ and $\frac{8 x}{15}$ .

$\frac{16 x^{2}}{9} + \frac{- 2 (8 x)}{15} + \frac{4}{25}$

Step 1.4.1.2

Multiply $8$ by $- 2$ .

$\frac{16 x^{2}}{9} + \frac{- 16 x}{15} + \frac{4}{25}$

Step 1.4.2

Move the negative in front of the fraction.

$\frac{16 x^{2}}{9} - \frac{16 x}{15} + \frac{4}{25}$

Step 2

The largest exponent is the degree of the polynomial.

$2$