Trigonometry Examples

${(2 x + 1)}^{4}$

Step 1

Use the Binomial Theorem.

${(2 x)}^{4} + 4 {(2 x)}^{3} \cdot 1 + 6 {(2 x)}^{2} \cdot 1^{2} + 4 (2 x) \cdot 1^{3} + 1^{4}$

Step 2

Simplify each term.

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Step 2.1

Apply the product rule to $2 x$ .

$2^{4} x^{4} + 4 {(2 x)}^{3} \cdot 1 + 6 {(2 x)}^{2} \cdot 1^{2} + 4 (2 x) \cdot 1^{3} + 1^{4}$

Step 2.2

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

$16 x^{4} + 4 {(2 x)}^{3} \cdot 1 + 6 {(2 x)}^{2} \cdot 1^{2} + 4 (2 x) \cdot 1^{3} + 1^{4}$

Step 2.3

Apply the product rule to $2 x$ .

$16 x^{4} + 4 (2^{3} x^{3}) \cdot 1 + 6 {(2 x)}^{2} \cdot 1^{2} + 4 (2 x) \cdot 1^{3} + 1^{4}$

Step 2.4

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

$16 x^{4} + 4 (8 x^{3}) \cdot 1 + 6 {(2 x)}^{2} \cdot 1^{2} + 4 (2 x) \cdot 1^{3} + 1^{4}$

Step 2.5

Multiply $8$ by $4$ .

$16 x^{4} + 32 x^{3} \cdot 1 + 6 {(2 x)}^{2} \cdot 1^{2} + 4 (2 x) \cdot 1^{3} + 1^{4}$

Step 2.6

Multiply $32$ by $1$ .

$16 x^{4} + 32 x^{3} + 6 {(2 x)}^{2} \cdot 1^{2} + 4 (2 x) \cdot 1^{3} + 1^{4}$

Step 2.7

Apply the product rule to $2 x$ .

$16 x^{4} + 32 x^{3} + 6 (2^{2} x^{2}) \cdot 1^{2} + 4 (2 x) \cdot 1^{3} + 1^{4}$

Step 2.8

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

$16 x^{4} + 32 x^{3} + 6 (4 x^{2}) \cdot 1^{2} + 4 (2 x) \cdot 1^{3} + 1^{4}$

Step 2.9

Multiply $4$ by $6$ .

$16 x^{4} + 32 x^{3} + 24 x^{2} \cdot 1^{2} + 4 (2 x) \cdot 1^{3} + 1^{4}$

Step 2.10

One to any power is one.

$16 x^{4} + 32 x^{3} + 24 x^{2} \cdot 1 + 4 (2 x) \cdot 1^{3} + 1^{4}$

Step 2.11

Multiply $24$ by $1$ .

$16 x^{4} + 32 x^{3} + 24 x^{2} + 4 (2 x) \cdot 1^{3} + 1^{4}$

Step 2.12

Multiply $2$ by $4$ .

$16 x^{4} + 32 x^{3} + 24 x^{2} + 8 x \cdot 1^{3} + 1^{4}$

Step 2.13

One to any power is one.

$16 x^{4} + 32 x^{3} + 24 x^{2} + 8 x \cdot 1 + 1^{4}$

Step 2.14

Multiply $8$ by $1$ .

$16 x^{4} + 32 x^{3} + 24 x^{2} + 8 x + 1^{4}$

Step 2.15

One to any power is one.

$16 x^{4} + 32 x^{3} + 24 x^{2} + 8 x + 1$