Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

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

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Step 2.1

Move $a$ .

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

Step 2.2

Multiply $a$ by $a$ .

$3 a^{2} b^{3} + 3 a b^{3} b$

Step 3

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

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Step 3.1

Move $b$ .

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

Step 3.2

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

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Step 3.2.1

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

$3 a^{2} b^{3} + 3 a (b^{1} b^{3})$

Step 3.2.2

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

$3 a^{2} b^{3} + 3 a b^{1 + 3}$

Step 3.3

Add $1$ and $3$ .

$3 a^{2} b^{3} + 3 a b^{4}$