Calculus Examples

${(2 + h)}^{4}$

Step 1

Use the Binomial Theorem.

$2^{4} + 4 \cdot 2^{3} h + 6 \cdot 2^{2} h^{2} + 4 \cdot 2 h^{3} + h^{4}$

Step 2

Simplify each term.

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Step 2.1

Raise $2$ to the power of $4$ .

$16 + 4 \cdot 2^{3} h + 6 \cdot 2^{2} h^{2} + 4 \cdot 2 h^{3} + h^{4}$

Step 2.2

Raise $2$ to the power of $3$ .

$16 + 4 \cdot 8 h + 6 \cdot 2^{2} h^{2} + 4 \cdot 2 h^{3} + h^{4}$

Step 2.3

Multiply $4$ by $8$ .

$16 + 32 h + 6 \cdot 2^{2} h^{2} + 4 \cdot 2 h^{3} + h^{4}$

Step 2.4

Raise $2$ to the power of $2$ .

$16 + 32 h + 6 \cdot 4 h^{2} + 4 \cdot 2 h^{3} + h^{4}$

Step 2.5

Multiply $6$ by $4$ .

$16 + 32 h + 24 h^{2} + 4 \cdot 2 h^{3} + h^{4}$

Step 2.6

Multiply $4$ by $2$ .

$16 + 32 h + 24 h^{2} + 8 h^{3} + h^{4}$