Calculus Examples

${(3 + h)}^{3}$

Step 1

Use the Binomial Theorem.

$3^{3} + 3 \cdot 3^{2} h + 3 \cdot 3 h^{2} + h^{3}$

Step 2

Simplify each term.

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Step 2.1

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

$27 + 3 \cdot 3^{2} h + 3 \cdot 3 h^{2} + h^{3}$

Step 2.2

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

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Step 2.2.1

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

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Step 2.2.1.1

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

$27 + 3^{1} \cdot 3^{2} h + 3 \cdot 3 h^{2} + h^{3}$

Step 2.2.1.2

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

$27 + 3^{1 + 2} h + 3 \cdot 3 h^{2} + h^{3}$

Step 2.2.2

Add $1$ and $2$ .

$27 + 3^{3} h + 3 \cdot 3 h^{2} + h^{3}$

Step 2.3

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

$27 + 27 h + 3 \cdot 3 h^{2} + h^{3}$

Step 2.4

Multiply $3$ by $3$ .

$27 + 27 h + 9 h^{2} + h^{3}$