Calculus Examples

${(2 x + 1)}^{3}$

Step 1

Use the Binomial Theorem.

${(2 x)}^{3} + 3 {(2 x)}^{2} \cdot 1 + 3 (2 x) \cdot 1^{2} + 1^{3}$

Step 2

Simplify each term.

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Step 2.1

Apply the product rule to $2 x$ .

$2^{3} x^{3} + 3 {(2 x)}^{2} \cdot 1 + 3 (2 x) \cdot 1^{2} + 1^{3}$

Step 2.2

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

$8 x^{3} + 3 {(2 x)}^{2} \cdot 1 + 3 (2 x) \cdot 1^{2} + 1^{3}$

Step 2.3

Apply the product rule to $2 x$ .

$8 x^{3} + 3 (2^{2} x^{2}) \cdot 1 + 3 (2 x) \cdot 1^{2} + 1^{3}$

Step 2.4

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

$8 x^{3} + 3 (4 x^{2}) \cdot 1 + 3 (2 x) \cdot 1^{2} + 1^{3}$

Step 2.5

Multiply $4$ by $3$ .

$8 x^{3} + 12 x^{2} \cdot 1 + 3 (2 x) \cdot 1^{2} + 1^{3}$

Step 2.6

Multiply $12$ by $1$ .

$8 x^{3} + 12 x^{2} + 3 (2 x) \cdot 1^{2} + 1^{3}$

Step 2.7

Multiply $2$ by $3$ .

$8 x^{3} + 12 x^{2} + 6 x \cdot 1^{2} + 1^{3}$

Step 2.8

One to any power is one.

$8 x^{3} + 12 x^{2} + 6 x \cdot 1 + 1^{3}$

Step 2.9

Multiply $6$ by $1$ .

$8 x^{3} + 12 x^{2} + 6 x + 1^{3}$

Step 2.10

One to any power is one.

$8 x^{3} + 12 x^{2} + 6 x + 1$