Find the Product (r^3-6t^4)(r^3+6t^4)

$(r^{3} - 6 t^{4}) (r^{3} + 6 t^{4})$

Expand $(r^{3} - 6 t^{4}) (r^{3} + 6 t^{4})$ using the FOIL Method.

Apply the distributive property.

$r^{3} (r^{3} + 6 t^{4}) - 6 t^{4} (r^{3} + 6 t^{4})$

Apply the distributive property.

$r^{3} r^{3} + r^{3} (6 t^{4}) - 6 t^{4} (r^{3} + 6 t^{4})$

Apply the distributive property.

$r^{3} r^{3} + r^{3} (6 t^{4}) - 6 t^{4} r^{3} - 6 t^{4} (6 t^{4})$

Simplify terms.

Combine the opposite terms in $r^{3} r^{3} + r^{3} (6 t^{4}) - 6 t^{4} r^{3} - 6 t^{4} (6 t^{4})$ .

Reorder the factors in the terms $r^{3} (6 t^{4})$ and $- 6 t^{4} r^{3}$ .

$r^{3} r^{3} + 6 t^{4} r^{3} - 6 t^{4} r^{3} - 6 t^{4} (6 t^{4})$

Subtract $6 t^{4} r^{3}$ from $6 t^{4} r^{3}$ .

$r^{3} r^{3} + 0 - 6 t^{4} (6 t^{4})$

Add $r^{3} r^{3}$ and $0$ .

$r^{3} r^{3} - 6 t^{4} (6 t^{4})$

Simplify each term.

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

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

$r^{3 + 3} - 6 t^{4} (6 t^{4})$

Add $3$ and $3$ .

$r^{6} - 6 t^{4} (6 t^{4})$

Rewrite using the commutative property of multiplication.

$r^{6} - 6 \cdot 6 t^{4} t^{4}$

Multiply $t^{4}$ by $t^{4}$ by adding the exponents.

Move $t^{4}$ .

$r^{6} - 6 \cdot 6 (t^{4} t^{4})$

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

$r^{6} - 6 \cdot 6 t^{4 + 4}$

Add $4$ and $4$ .

$r^{6} - 6 \cdot 6 t^{8}$

Multiply $- 6$ by $6$ .

$r^{6} - 36 t^{8}$