Trigonometry Examples

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

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

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}

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

Step 2

Simplify each term.

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Step 2.1

Apply the product rule to

2 x

$2 x$ .

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}

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

Step 2.2

Raise

2

$2$ to the power of

4

$4$ .

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

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

Step 2.3

Apply the product rule to

2 x

$2 x$ .

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}

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

Step 2.4

Raise

2

$2$ to the power of

3

$3$ .

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

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

Step 2.5

Multiply

8

$8$ by

4

$4$ .

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

$32$ by

1

$1$ .

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

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

Step 2.7

Apply the product rule to

2 x

$2 x$ .

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

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

Step 2.8

Raise

2

$2$ to the power of

2

$2$ .

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

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

Step 2.9

Multiply

4

$4$ by

6

$6$ .

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

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

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}

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

Step 2.11

Multiply

24

$24$ by

1

$1$ .

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

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

Step 2.12

Multiply

2

$2$ by

4

$4$ .

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

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

Step 2.14

Multiply

8

$8$ by

1

$1$ .

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

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

Step 2.15

One to any power is one.

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

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

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

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