Algebra Examples

$(\frac{5}{7} x - \frac{1}{3} y) (\frac{5}{7} x + \frac{1}{3} y)$

Step 1

Simplify terms.

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{5}{7}$ and $x$ .

$(\frac{5 x}{7} - \frac{1}{3} y) (\frac{5}{7} x + \frac{1}{3} y)$

Step 1.1.2

Combine $y$ and $\frac{1}{3}$ .

$(\frac{5 x}{7} - \frac{y}{3}) (\frac{5}{7} x + \frac{1}{3} y)$

Step 1.2

Simplify each term.

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Step 1.2.1

Combine $\frac{5}{7}$ and $x$ .

$(\frac{5 x}{7} - \frac{y}{3}) (\frac{5 x}{7} + \frac{1}{3} y)$

Step 1.2.2

Combine $\frac{1}{3}$ and $y$ .

$(\frac{5 x}{7} - \frac{y}{3}) (\frac{5 x}{7} + \frac{y}{3})$

Step 2

Expand $(\frac{5 x}{7} - \frac{y}{3}) (\frac{5 x}{7} + \frac{y}{3})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$\frac{5 x}{7} (\frac{5 x}{7} + \frac{y}{3}) - \frac{y}{3} (\frac{5 x}{7} + \frac{y}{3})$

Step 2.2

Apply the distributive property.

$\frac{5 x}{7} \cdot \frac{5 x}{7} + \frac{5 x}{7} \cdot \frac{y}{3} - \frac{y}{3} (\frac{5 x}{7} + \frac{y}{3})$

Step 2.3

Apply the distributive property.

$\frac{5 x}{7} \cdot \frac{5 x}{7} + \frac{5 x}{7} \cdot \frac{y}{3} - \frac{y}{3} \cdot \frac{5 x}{7} - \frac{y}{3} \cdot \frac{y}{3}$

Step 3

Simplify terms.

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Step 3.1

Combine the opposite terms in $\frac{5 x}{7} \cdot \frac{5 x}{7} + \frac{5 x}{7} \cdot \frac{y}{3} - \frac{y}{3} \cdot \frac{5 x}{7} - \frac{y}{3} \cdot \frac{y}{3}$ .

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Step 3.1.1

Reorder the factors in the terms $\frac{5 x}{7} \cdot \frac{y}{3}$ and $- \frac{y}{3} \cdot \frac{5 x}{7}$ .

$\frac{5 x}{7} \cdot \frac{5 x}{7} + \frac{5 x}{7} \cdot \frac{y}{3} - \frac{5 x}{7} \cdot \frac{y}{3} - \frac{y}{3} \cdot \frac{y}{3}$

Step 3.1.2

Subtract $\frac{5 x}{7} \cdot \frac{y}{3}$ from $\frac{5 x}{7} \cdot \frac{y}{3}$ .

$\frac{5 x}{7} \cdot \frac{5 x}{7} + 0 - \frac{y}{3} \cdot \frac{y}{3}$

Step 3.1.3

Add $\frac{5 x}{7} \cdot \frac{5 x}{7}$ and $0$ .

$\frac{5 x}{7} \cdot \frac{5 x}{7} - \frac{y}{3} \cdot \frac{y}{3}$

Step 3.2

Simplify each term.

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Step 3.2.1

Multiply $\frac{5 x}{7} \cdot \frac{5 x}{7}$ .

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Step 3.2.1.1

Multiply $\frac{5 x}{7}$ by $\frac{5 x}{7}$ .

$\frac{5 x (5 x)}{7 \cdot 7} - \frac{y}{3} \cdot \frac{y}{3}$

Step 3.2.1.2

Multiply $5$ by $5$ .

$\frac{25 x \cdot x}{7 \cdot 7} - \frac{y}{3} \cdot \frac{y}{3}$

Step 3.2.1.3

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

$\frac{25 (x^{1} x)}{7 \cdot 7} - \frac{y}{3} \cdot \frac{y}{3}$

Step 3.2.1.4

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

$\frac{25 (x^{1} x^{1})}{7 \cdot 7} - \frac{y}{3} \cdot \frac{y}{3}$

Step 3.2.1.5

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

$\frac{25 x^{1 + 1}}{7 \cdot 7} - \frac{y}{3} \cdot \frac{y}{3}$

Step 3.2.1.6

Add $1$ and $1$ .

$\frac{25 x^{2}}{7 \cdot 7} - \frac{y}{3} \cdot \frac{y}{3}$

Step 3.2.1.7

Multiply $7$ by $7$ .

$\frac{25 x^{2}}{49} - \frac{y}{3} \cdot \frac{y}{3}$

Step 3.2.2

Multiply $- \frac{y}{3} \cdot \frac{y}{3}$ .

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Step 3.2.2.1

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

$\frac{25 x^{2}}{49} - \frac{y \cdot y}{3 \cdot 3}$

Step 3.2.2.2

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

$\frac{25 x^{2}}{49} - \frac{y^{1} y}{3 \cdot 3}$

Step 3.2.2.3

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

$\frac{25 x^{2}}{49} - \frac{y^{1} y^{1}}{3 \cdot 3}$

Step 3.2.2.4

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

$\frac{25 x^{2}}{49} - \frac{y^{1 + 1}}{3 \cdot 3}$

Step 3.2.2.5

Add $1$ and $1$ .

$\frac{25 x^{2}}{49} - \frac{y^{2}}{3 \cdot 3}$

Step 3.2.2.6

Multiply $3$ by $3$ .

$\frac{25 x^{2}}{49} - \frac{y^{2}}{9}$