Simplify (3/7m^3+1/4n^3)(3/7m^3-1/4n^3)

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

Step 1

Simplify terms.

Simplify each term.

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

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

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

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

Simplify each term.

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

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

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.

Apply the distributive property.

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

Apply the distributive property.

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

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.

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

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

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

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

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

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

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

Simplify each term.

Combine.

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

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

Move $m^{3}$ .

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

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

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

Add $3$ and $3$ .

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

Multiply $3$ by $3$ .

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

Multiply $7$ by $7$ .

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

Rewrite using the commutative property of multiplication.

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

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

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

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

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

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

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

Add $3$ and $3$ .

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

Multiply $4$ by $4$ .

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

Simplify (3/7m^3+1/4n^3)(3/7m^3-1/4n^3)

Related Questions

Support LCMGCF.com by disabling your adblocker.