Simplify (5a-b^3)(b^3+5a)

$(5 a - b^{3}) (b^{3} + 5 a)$

Expand $(5 a - b^{3}) (b^{3} + 5 a)$ using the FOIL Method.

Apply the distributive property.

$5 a (b^{3} + 5 a) - b^{3} (b^{3} + 5 a)$

Apply the distributive property.

$5 a b^{3} + 5 a (5 a) - b^{3} (b^{3} + 5 a)$

Apply the distributive property.

$5 a b^{3} + 5 a (5 a) - b^{3} b^{3} - b^{3} (5 a)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 a b^{3} + 5 \cdot 5 a \cdot a - b^{3} b^{3} - b^{3} (5 a)$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$5 a b^{3} + 5 \cdot 5 (a \cdot a) - b^{3} b^{3} - b^{3} (5 a)$

Multiply $a$ by $a$ .

$5 a b^{3} + 5 \cdot 5 a^{2} - b^{3} b^{3} - b^{3} (5 a)$

Multiply $5$ by $5$ .

$5 a b^{3} + 25 a^{2} - b^{3} b^{3} - b^{3} (5 a)$

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

Move $b^{3}$ .

$5 a b^{3} + 25 a^{2} - (b^{3} b^{3}) - b^{3} (5 a)$

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

$5 a b^{3} + 25 a^{2} - b^{3 + 3} - b^{3} (5 a)$

Add $3$ and $3$ .

$5 a b^{3} + 25 a^{2} - b^{6} - b^{3} (5 a)$

Rewrite using the commutative property of multiplication.

$5 a b^{3} + 25 a^{2} - b^{6} - 1 \cdot 5 b^{3} a$

Multiply $- 1$ by $5$ .

$5 a b^{3} + 25 a^{2} - b^{6} - 5 b^{3} a$

Subtract $5 b^{3} a$ from $5 a b^{3}$ .

Move $b^{3}$ .

$25 a^{2} - b^{6} + 5 a b^{3} - 5 a b^{3}$

Subtract $5 a b^{3}$ from $5 a b^{3}$ .

$25 a^{2} - b^{6} + 0$

Add $25 a^{2}$ and $0$ .

$- b^{6} + 25 a^{2}$