Basic Math Examples

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

Step 1

Apply the distributive property.

$3 a^{2} b a + 3 a^{2} b (4 b) + 3 a^{2} b (3 a^{3}) + 3 a^{2} b \cdot b^{2}$

Step 2

Simplify.

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Step 2.1

Multiply $a^{2}$ by $a$ by adding the exponents.

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Step 2.1.1

Move $a$ .

$3 (a \cdot a^{2}) b + 3 a^{2} b (4 b) + 3 a^{2} b (3 a^{3}) + 3 a^{2} b \cdot b^{2}$

Step 2.1.2

Multiply $a$ by $a^{2}$ .

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Step 2.1.2.1

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

$3 (a^{1} a^{2}) b + 3 a^{2} b (4 b) + 3 a^{2} b (3 a^{3}) + 3 a^{2} b \cdot b^{2}$

Step 2.1.2.2

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

$3 a^{1 + 2} b + 3 a^{2} b (4 b) + 3 a^{2} b (3 a^{3}) + 3 a^{2} b \cdot b^{2}$

Step 2.1.3

Add $1$ and $2$ .

$3 a^{3} b + 3 a^{2} b (4 b) + 3 a^{2} b (3 a^{3}) + 3 a^{2} b \cdot b^{2}$

Step 2.2

Multiply $b$ by $b$ by adding the exponents.

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Step 2.2.1

Move $b$ .

$3 a^{3} b + 3 a^{2} (b \cdot b) \cdot 4 + 3 a^{2} b (3 a^{3}) + 3 a^{2} b \cdot b^{2}$

Step 2.2.2

Multiply $b$ by $b$ .

$3 a^{3} b + 3 a^{2} b^{2} \cdot 4 + 3 a^{2} b (3 a^{3}) + 3 a^{2} b \cdot b^{2}$

Step 2.3

Multiply $a^{2}$ by $a^{3}$ by adding the exponents.

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Step 2.3.1

Move $a^{3}$ .

$3 a^{3} b + 3 a^{2} b^{2} \cdot 4 + 3 (a^{3} a^{2}) b \cdot 3 + 3 a^{2} b \cdot b^{2}$

Step 2.3.2

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

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

Step 2.3.3

Add $3$ and $2$ .

$3 a^{3} b + 3 a^{2} b^{2} \cdot 4 + 3 a^{5} b \cdot 3 + 3 a^{2} b \cdot b^{2}$

Step 2.4

Multiply $b$ by $b^{2}$ by adding the exponents.

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Step 2.4.1

Move $b^{2}$ .

$3 a^{3} b + 3 a^{2} b^{2} \cdot 4 + 3 a^{5} b \cdot 3 + 3 a^{2} (b^{2} b)$

Step 2.4.2

Multiply $b^{2}$ by $b$ .

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Step 2.4.2.1

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

$3 a^{3} b + 3 a^{2} b^{2} \cdot 4 + 3 a^{5} b \cdot 3 + 3 a^{2} (b^{2} b^{1})$

Step 2.4.2.2

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

$3 a^{3} b + 3 a^{2} b^{2} \cdot 4 + 3 a^{5} b \cdot 3 + 3 a^{2} b^{2 + 1}$

Step 2.4.3

Add $2$ and $1$ .

$3 a^{3} b + 3 a^{2} b^{2} \cdot 4 + 3 a^{5} b \cdot 3 + 3 a^{2} b^{3}$

Step 3

Simplify each term.

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Step 3.1

Multiply $4$ by $3$ .

$3 a^{3} b + 12 a^{2} b^{2} + 3 a^{5} b \cdot 3 + 3 a^{2} b^{3}$

Step 3.2

Multiply $3$ by $3$ .

$3 a^{3} b + 12 a^{2} b^{2} + 9 a^{5} b + 3 a^{2} b^{3}$