Algebra Examples

$3 a^{3} (8 a + b)$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$3 a^{3} (8 a) + 3 a^{3} b$

Step 1.2

Rewrite using the commutative property of multiplication.

$3 \cdot 8 a^{3} a + 3 a^{3} b$

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

Move $a$ .

$3 \cdot 8 (a \cdot a^{3}) + 3 a^{3} b$

Step 2.1.2

Multiply $a$ by $a^{3}$ .

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Step 2.1.2.1

Raise $a$ to the power of $1$ .

$3 \cdot 8 (a^{1} a^{3}) + 3 a^{3} b$

Step 2.1.2.2

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

$3 \cdot 8 a^{1 + 3} + 3 a^{3} b$

Step 2.1.3

Add $1$ and $3$ .

$3 \cdot 8 a^{4} + 3 a^{3} b$

Step 2.2

Multiply $3$ by $8$ .

$24 a^{4} + 3 a^{3} b$