Multiply (a+(b+3))^3

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

Remove parentheses.

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

Use the Multinomial Theorem.

$a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} + 3 a^{2} \cdot 3 + 6 a b \cdot 3 + 3 b^{2} \cdot 3 + 3 a \cdot 3^{2} + 3 b \cdot 3^{2} + 3^{3}$

Simplify each term.

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Multiply $3$ by $3$ .

$a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} + 9 a^{2} + 6 a b \cdot 3 + 3 b^{2} \cdot 3 + 3 a \cdot 3^{2} + 3 b \cdot 3^{2} + 3^{3}$

Multiply $3$ by $6$ .

$a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} + 9 a^{2} + 18 a b + 3 b^{2} \cdot 3 + 3 a \cdot 3^{2} + 3 b \cdot 3^{2} + 3^{3}$

Multiply $3$ by $3$ .

$a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} + 9 a^{2} + 18 a b + 9 b^{2} + 3 a \cdot 3^{2} + 3 b \cdot 3^{2} + 3^{3}$

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

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Move $3^{2}$ .

$a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} + 9 a^{2} + 18 a b + 9 b^{2} + 3^{2} \cdot 3 a + 3 b \cdot 3^{2} + 3^{3}$

Multiply $3^{2}$ by $3$ .

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Raise $3$ to the power of $1$ .

$a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} + 9 a^{2} + 18 a b + 9 b^{2} + 3^{2} \cdot 3^{1} a + 3 b \cdot 3^{2} + 3^{3}$

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

$a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} + 9 a^{2} + 18 a b + 9 b^{2} + 3^{2 + 1} a + 3 b \cdot 3^{2} + 3^{3}$

Add $2$ and $1$ .

$a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} + 9 a^{2} + 18 a b + 9 b^{2} + 3^{3} a + 3 b \cdot 3^{2} + 3^{3}$

Raise $3$ to the power of $3$ .

$a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} + 9 a^{2} + 18 a b + 9 b^{2} + 27 a + 3 b \cdot 3^{2} + 3^{3}$

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

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Move $3^{2}$ .

$a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} + 9 a^{2} + 18 a b + 9 b^{2} + 27 a + 3^{2} \cdot 3 b + 3^{3}$

Multiply $3^{2}$ by $3$ .

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Raise $3$ to the power of $1$ .

$a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} + 9 a^{2} + 18 a b + 9 b^{2} + 27 a + 3^{2} \cdot 3^{1} b + 3^{3}$

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

$a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} + 9 a^{2} + 18 a b + 9 b^{2} + 27 a + 3^{2 + 1} b + 3^{3}$

Add $2$ and $1$ .

$a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} + 9 a^{2} + 18 a b + 9 b^{2} + 27 a + 3^{3} b + 3^{3}$

Raise $3$ to the power of $3$ .

$a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} + 9 a^{2} + 18 a b + 9 b^{2} + 27 a + 27 b + 3^{3}$

Raise $3$ to the power of $3$ .

$a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} + 9 a^{2} + 18 a b + 9 b^{2} + 27 a + 27 b + 27$

Multiply (a+(b+3))^3

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