Calculus Examples

${(2 + h)}^{3} - 8$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Use the Binomial Theorem.

$2^{3} + 3 \cdot 2^{2} h + 3 \cdot 2 h^{2} + h^{3} - 8$

Step 1.2

Simplify each term.

Tap for more steps...

Step 1.2.1

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

$8 + 3 \cdot 2^{2} h + 3 \cdot 2 h^{2} + h^{3} - 8$

Step 1.2.2

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

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

Step 1.2.3

Multiply $3$ by $4$ .

$8 + 12 h + 3 \cdot 2 h^{2} + h^{3} - 8$

Step 1.2.4

Multiply $3$ by $2$ .

$8 + 12 h + 6 h^{2} + h^{3} - 8$

Step 2

Combine the opposite terms in $8 + 12 h + 6 h^{2} + h^{3} - 8$ .

Tap for more steps...

Step 2.1

Subtract $8$ from $8$ .

$12 h + 6 h^{2} + h^{3} + 0$

Step 2.2

Add $12 h + 6 h^{2} + h^{3}$ and $0$ .

$12 h + 6 h^{2} + h^{3}$