Basic Math Examples

$(\frac{8}{7} - \frac{4 m}{7}) (\frac{8}{5} + \frac{4 m}{5})$

Step 1

Expand $(\frac{8}{7} - \frac{4 m}{7}) (\frac{8}{5} + \frac{4 m}{5})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$\frac{8}{7} (\frac{8}{5} + \frac{4 m}{5}) - \frac{4 m}{7} (\frac{8}{5} + \frac{4 m}{5})$

Step 1.2

Apply the distributive property.

$\frac{8}{7} \cdot \frac{8}{5} + \frac{8}{7} \cdot \frac{4 m}{5} - \frac{4 m}{7} (\frac{8}{5} + \frac{4 m}{5})$

Step 1.3

Apply the distributive property.

$\frac{8}{7} \cdot \frac{8}{5} + \frac{8}{7} \cdot \frac{4 m}{5} - \frac{4 m}{7} \cdot \frac{8}{5} - \frac{4 m}{7} \cdot \frac{4 m}{5}$

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 $\frac{8}{7} \cdot \frac{8}{5}$ .

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Step 2.1.1.1

Multiply $\frac{8}{7}$ by $\frac{8}{5}$ .

$\frac{8 \cdot 8}{7 \cdot 5} + \frac{8}{7} \cdot \frac{4 m}{5} - \frac{4 m}{7} \cdot \frac{8}{5} - \frac{4 m}{7} \cdot \frac{4 m}{5}$

Step 2.1.1.2

Multiply $8$ by $8$ .

$\frac{64}{7 \cdot 5} + \frac{8}{7} \cdot \frac{4 m}{5} - \frac{4 m}{7} \cdot \frac{8}{5} - \frac{4 m}{7} \cdot \frac{4 m}{5}$

Step 2.1.1.3

Multiply $7$ by $5$ .

$\frac{64}{35} + \frac{8}{7} \cdot \frac{4 m}{5} - \frac{4 m}{7} \cdot \frac{8}{5} - \frac{4 m}{7} \cdot \frac{4 m}{5}$

Step 2.1.2

Multiply $\frac{8}{7} \cdot \frac{4 m}{5}$ .

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Step 2.1.2.1

Multiply $\frac{8}{7}$ by $\frac{4 m}{5}$ .

$\frac{64}{35} + \frac{8 (4 m)}{7 \cdot 5} - \frac{4 m}{7} \cdot \frac{8}{5} - \frac{4 m}{7} \cdot \frac{4 m}{5}$

Step 2.1.2.2

Multiply $4$ by $8$ .

$\frac{64}{35} + \frac{32 m}{7 \cdot 5} - \frac{4 m}{7} \cdot \frac{8}{5} - \frac{4 m}{7} \cdot \frac{4 m}{5}$

Step 2.1.2.3

Multiply $7$ by $5$ .

$\frac{64}{35} + \frac{32 m}{35} - \frac{4 m}{7} \cdot \frac{8}{5} - \frac{4 m}{7} \cdot \frac{4 m}{5}$

Step 2.1.3

Multiply $- \frac{4 m}{7} \cdot \frac{8}{5}$ .

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Step 2.1.3.1

Multiply $\frac{8}{5}$ by $\frac{4 m}{7}$ .

$\frac{64}{35} + \frac{32 m}{35} - \frac{8 (4 m)}{5 \cdot 7} - \frac{4 m}{7} \cdot \frac{4 m}{5}$

Step 2.1.3.2

Multiply $4$ by $8$ .

$\frac{64}{35} + \frac{32 m}{35} - \frac{32 m}{5 \cdot 7} - \frac{4 m}{7} \cdot \frac{4 m}{5}$

Step 2.1.3.3

Multiply $5$ by $7$ .

$\frac{64}{35} + \frac{32 m}{35} - \frac{32 m}{35} - \frac{4 m}{7} \cdot \frac{4 m}{5}$

Step 2.1.4

Multiply $- \frac{4 m}{7} \cdot \frac{4 m}{5}$ .

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Step 2.1.4.1

Multiply $\frac{4 m}{5}$ by $\frac{4 m}{7}$ .

$\frac{64}{35} + \frac{32 m}{35} - \frac{32 m}{35} - \frac{4 m (4 m)}{5 \cdot 7}$

Step 2.1.4.2

Multiply $4$ by $4$ .

$\frac{64}{35} + \frac{32 m}{35} - \frac{32 m}{35} - \frac{16 m \cdot m}{5 \cdot 7}$

Step 2.1.4.3

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

$\frac{64}{35} + \frac{32 m}{35} - \frac{32 m}{35} - \frac{16 (m^{1} m)}{5 \cdot 7}$

Step 2.1.4.4

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

$\frac{64}{35} + \frac{32 m}{35} - \frac{32 m}{35} - \frac{16 (m^{1} m^{1})}{5 \cdot 7}$

Step 2.1.4.5

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

$\frac{64}{35} + \frac{32 m}{35} - \frac{32 m}{35} - \frac{16 m^{1 + 1}}{5 \cdot 7}$

Step 2.1.4.6

Add $1$ and $1$ .

$\frac{64}{35} + \frac{32 m}{35} - \frac{32 m}{35} - \frac{16 m^{2}}{5 \cdot 7}$

Step 2.1.4.7

Multiply $5$ by $7$ .

$\frac{64}{35} + \frac{32 m}{35} - \frac{32 m}{35} - \frac{16 m^{2}}{35}$

Step 2.2

Subtract $\frac{32 m}{35}$ from $\frac{32 m}{35}$ .

$\frac{64}{35} + 0 - \frac{16 m^{2}}{35}$

Step 2.3

Add $\frac{64}{35}$ and $0$ .

$\frac{64}{35} - \frac{16 m^{2}}{35}$