Pre-Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $x$ by $x$ .

$x^{2} + x \frac{3}{7} + \frac{5}{7} x + \frac{5}{7} \cdot \frac{3}{7}$

Step 2.1.2

Combine $x$ and $\frac{3}{7}$ .

$x^{2} + \frac{x \cdot 3}{7} + \frac{5}{7} x + \frac{5}{7} \cdot \frac{3}{7}$

Step 2.1.3

Move $3$ to the left of $x$ .

$x^{2} + \frac{3 \cdot x}{7} + \frac{5}{7} x + \frac{5}{7} \cdot \frac{3}{7}$

Step 2.1.4

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

$x^{2} + \frac{3 x}{7} + \frac{5 x}{7} + \frac{5}{7} \cdot \frac{3}{7}$

Step 2.1.5

Multiply $\frac{5}{7} \cdot \frac{3}{7}$ .

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Step 2.1.5.1

Multiply $\frac{5}{7}$ by $\frac{3}{7}$ .

$x^{2} + \frac{3 x}{7} + \frac{5 x}{7} + \frac{5 \cdot 3}{7 \cdot 7}$

Step 2.1.5.2

Multiply $5$ by $3$ .

$x^{2} + \frac{3 x}{7} + \frac{5 x}{7} + \frac{15}{7 \cdot 7}$

Step 2.1.5.3

Multiply $7$ by $7$ .

$x^{2} + \frac{3 x}{7} + \frac{5 x}{7} + \frac{15}{49}$

Step 2.2

Combine the numerators over the common denominator.

$x^{2} + \frac{3 x + 5 x}{7} + \frac{15}{49}$

Step 3

Add $3 x$ and $5 x$ .

$x^{2} + \frac{8 x}{7} + \frac{15}{49}$