Algebra Examples

$(\frac{3}{7} m^{3} + \frac{1}{4} n^{3}) (\frac{3}{7} m^{3} - \frac{1}{4} n^{3})$

Step 1

Simplify terms.

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{3}{7}$ and $m^{3}$ .

$(\frac{3 m^{3}}{7} + \frac{1}{4} n^{3}) (\frac{3}{7} m^{3} - \frac{1}{4} n^{3})$

Step 1.1.2

Combine $\frac{1}{4}$ and $n^{3}$ .

$(\frac{3 m^{3}}{7} + \frac{n^{3}}{4}) (\frac{3}{7} m^{3} - \frac{1}{4} n^{3})$

Step 1.2

Simplify each term.

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Step 1.2.1

Combine $\frac{3}{7}$ and $m^{3}$ .

$(\frac{3 m^{3}}{7} + \frac{n^{3}}{4}) (\frac{3 m^{3}}{7} - \frac{1}{4} n^{3})$

Step 1.2.2

Combine $n^{3}$ and $\frac{1}{4}$ .

$(\frac{3 m^{3}}{7} + \frac{n^{3}}{4}) (\frac{3 m^{3}}{7} - \frac{n^{3}}{4})$

Step 2

Expand $(\frac{3 m^{3}}{7} + \frac{n^{3}}{4}) (\frac{3 m^{3}}{7} - \frac{n^{3}}{4})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$\frac{3 m^{3}}{7} (\frac{3 m^{3}}{7} - \frac{n^{3}}{4}) + \frac{n^{3}}{4} (\frac{3 m^{3}}{7} - \frac{n^{3}}{4})$

Step 2.2

Apply the distributive property.

$\frac{3 m^{3}}{7} \cdot \frac{3 m^{3}}{7} + \frac{3 m^{3}}{7} (- \frac{n^{3}}{4}) + \frac{n^{3}}{4} (\frac{3 m^{3}}{7} - \frac{n^{3}}{4})$

Step 2.3

Apply the distributive property.

$\frac{3 m^{3}}{7} \cdot \frac{3 m^{3}}{7} + \frac{3 m^{3}}{7} (- \frac{n^{3}}{4}) + \frac{n^{3}}{4} \cdot \frac{3 m^{3}}{7} + \frac{n^{3}}{4} (- \frac{n^{3}}{4})$

Step 3

Simplify terms.

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Step 3.1

Combine the opposite terms in $\frac{3 m^{3}}{7} \cdot \frac{3 m^{3}}{7} + \frac{3 m^{3}}{7} (- \frac{n^{3}}{4}) + \frac{n^{3}}{4} \cdot \frac{3 m^{3}}{7} + \frac{n^{3}}{4} (- \frac{n^{3}}{4})$ .

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Step 3.1.1

Reorder the factors in the terms $\frac{3 m^{3}}{7} (- \frac{n^{3}}{4})$ and $\frac{n^{3}}{4} \cdot \frac{3 m^{3}}{7}$ .

$\frac{3 m^{3}}{7} \cdot \frac{3 m^{3}}{7} - \frac{3 m^{3}}{7} \cdot \frac{n^{3}}{4} + \frac{3 m^{3}}{7} \cdot \frac{n^{3}}{4} + \frac{n^{3}}{4} (- \frac{n^{3}}{4})$

Step 3.1.2

Add $- \frac{3 m^{3}}{7} \cdot \frac{n^{3}}{4}$ and $\frac{3 m^{3}}{7} \cdot \frac{n^{3}}{4}$ .

$\frac{3 m^{3}}{7} \cdot \frac{3 m^{3}}{7} + 0 + \frac{n^{3}}{4} (- \frac{n^{3}}{4})$

Step 3.1.3

Add $\frac{3 m^{3}}{7} \cdot \frac{3 m^{3}}{7}$ and $0$ .

$\frac{3 m^{3}}{7} \cdot \frac{3 m^{3}}{7} + \frac{n^{3}}{4} (- \frac{n^{3}}{4})$

Step 3.2

Simplify each term.

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Step 3.2.1

Combine.

$\frac{3 m^{3} (3 m^{3})}{7 \cdot 7} + \frac{n^{3}}{4} (- \frac{n^{3}}{4})$

Step 3.2.2

Multiply $m^{3}$ by $m^{3}$ by adding the exponents.

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Step 3.2.2.1

Move $m^{3}$ .

$\frac{3 (m^{3} m^{3}) \cdot 3}{7 \cdot 7} + \frac{n^{3}}{4} (- \frac{n^{3}}{4})$

Step 3.2.2.2

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

$\frac{3 m^{3 + 3} \cdot 3}{7 \cdot 7} + \frac{n^{3}}{4} (- \frac{n^{3}}{4})$

Step 3.2.2.3

Add $3$ and $3$ .

$\frac{3 m^{6} \cdot 3}{7 \cdot 7} + \frac{n^{3}}{4} (- \frac{n^{3}}{4})$

Step 3.2.3

Multiply $3$ by $3$ .

$\frac{9 m^{6}}{7 \cdot 7} + \frac{n^{3}}{4} (- \frac{n^{3}}{4})$

Step 3.2.4

Multiply $7$ by $7$ .

$\frac{9 m^{6}}{49} + \frac{n^{3}}{4} (- \frac{n^{3}}{4})$

Step 3.2.5

Rewrite using the commutative property of multiplication.

$\frac{9 m^{6}}{49} - \frac{n^{3}}{4} \cdot \frac{n^{3}}{4}$

Step 3.2.6

Multiply $- \frac{n^{3}}{4} \cdot \frac{n^{3}}{4}$ .

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Step 3.2.6.1

Multiply $\frac{n^{3}}{4}$ by $\frac{n^{3}}{4}$ .

$\frac{9 m^{6}}{49} - \frac{n^{3} n^{3}}{4 \cdot 4}$

Step 3.2.6.2

Multiply $n^{3}$ by $n^{3}$ by adding the exponents.

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Step 3.2.6.2.1

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

$\frac{9 m^{6}}{49} - \frac{n^{3 + 3}}{4 \cdot 4}$

Step 3.2.6.2.2

Add $3$ and $3$ .

$\frac{9 m^{6}}{49} - \frac{n^{6}}{4 \cdot 4}$

Step 3.2.6.3

Multiply $4$ by $4$ .

$\frac{9 m^{6}}{49} - \frac{n^{6}}{16}$