Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

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

Rewrite using the commutative property of multiplication.

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

Step 2.1.2

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

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Step 2.1.2.1

Move $a$ .

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

Step 2.1.2.2

Multiply $a$ by $a$ .

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

Step 2.1.3

Multiply $5$ by $5$ .

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

Step 2.1.4

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

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Step 2.1.4.1

Move $b^{3}$ .

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

Step 2.1.4.2

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

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

Step 2.1.4.3

Add $3$ and $3$ .

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

Step 2.1.5

Rewrite using the commutative property of multiplication.

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

Step 2.1.6

Multiply $- 1$ by $5$ .

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

Step 2.2

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

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Step 2.2.1

Move $b^{3}$ .

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

Step 2.2.2

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

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

Step 2.3

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

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