Trigonometry Examples

7 x (2) (x^{2} + 1) (2 x) - {(x^{2} + 1)}^{2} \cdot 7

$7 x (2) (x^{2} + 1) (2 x) - {(x^{2} + 1)}^{2} \cdot 7$

Step 1

Multiply

7 x

$7 x$ by

2

$2$ .

7 x \cdot 2 (x^{2} + 1) (2 x) - {(x^{2} + 1)}^{2} \cdot 7

$7 x \cdot 2 (x^{2} + 1) (2 x) - {(x^{2} + 1)}^{2} \cdot 7$

Step 2

Factor

x^{2} + 1

$x^{2} + 1$ out of

7 x \cdot 2 (x^{2} + 1) (2 x) - {(x^{2} + 1)}^{2} \cdot 7

$7 x \cdot 2 (x^{2} + 1) (2 x) - {(x^{2} + 1)}^{2} \cdot 7$ .

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Step 2.1

Factor

x^{2} + 1

$x^{2} + 1$ out of

7 x \cdot 2 (x^{2} + 1) (2 x)

$7 x \cdot 2 (x^{2} + 1) (2 x)$ .

(x^{2} + 1) (7 x \cdot 2 (2 x)) - {(x^{2} + 1)}^{2} \cdot 7

$(x^{2} + 1) (7 x \cdot 2 (2 x)) - {(x^{2} + 1)}^{2} \cdot 7$

Step 2.2

Factor

x^{2} + 1

$x^{2} + 1$ out of

- {(x^{2} + 1)}^{2} \cdot 7

$- {(x^{2} + 1)}^{2} \cdot 7$ .

(x^{2} + 1) (7 x \cdot 2 (2 x)) + (x^{2} + 1) (- (x^{2} + 1) \cdot 7)

$(x^{2} + 1) (7 x \cdot 2 (2 x)) + (x^{2} + 1) (- (x^{2} + 1) \cdot 7)$

Step 2.3

Factor

x^{2} + 1

$x^{2} + 1$ out of

(x^{2} + 1) (7 x \cdot 2 (2 x)) + (x^{2} + 1) (- (x^{2} + 1) \cdot 7)

$(x^{2} + 1) (7 x \cdot 2 (2 x)) + (x^{2} + 1) (- (x^{2} + 1) \cdot 7)$ .

(x^{2} + 1) (7 x \cdot 2 (2 x) - (x^{2} + 1) \cdot 7)

$(x^{2} + 1) (7 x \cdot 2 (2 x) - (x^{2} + 1) \cdot 7)$

(x^{2} + 1) (7 x \cdot 2 (2 x) - (x^{2} + 1) \cdot 7)

$(x^{2} + 1) (7 x \cdot 2 (2 x) - (x^{2} + 1) \cdot 7)$

Step 3

Multiply

x

$x$ by

x

$x$ by adding the exponents.

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Step 3.1

Move

x

$x$ .

(x^{2} + 1) (7 (x \cdot x) \cdot 2 \cdot 2 - (x^{2} + 1) \cdot 7)

$(x^{2} + 1) (7 (x \cdot x) \cdot 2 \cdot 2 - (x^{2} + 1) \cdot 7)$

Step 3.2

Multiply

x

$x$ by

x

$x$ .

(x^{2} + 1) (7 x^{2} \cdot 2 \cdot 2 - (x^{2} + 1) \cdot 7)

$(x^{2} + 1) (7 x^{2} \cdot 2 \cdot 2 - (x^{2} + 1) \cdot 7)$

(x^{2} + 1) (7 x^{2} \cdot 2 \cdot 2 - (x^{2} + 1) \cdot 7)

$(x^{2} + 1) (7 x^{2} \cdot 2 \cdot 2 - (x^{2} + 1) \cdot 7)$

Step 4

Multiply

2

$2$ by

7

$7$ .

(x^{2} + 1) (14 x^{2} \cdot 2 - (x^{2} + 1) \cdot 7)

$(x^{2} + 1) (14 x^{2} \cdot 2 - (x^{2} + 1) \cdot 7)$

Step 5

Multiply

2

$2$ by

14

$14$ .

(x^{2} + 1) (28 x^{2} - (x^{2} + 1) \cdot 7)

$(x^{2} + 1) (28 x^{2} - (x^{2} + 1) \cdot 7)$

Step 6

Apply the distributive property.

(x^{2} + 1) (28 x^{2} + (- x^{2} - 1 \cdot 1) \cdot 7)

$(x^{2} + 1) (28 x^{2} + (- x^{2} - 1 \cdot 1) \cdot 7)$

Step 7

Multiply

- 1

$- 1$ by

1

$1$ .

(x^{2} + 1) (28 x^{2} + (- x^{2} - 1) \cdot 7)

$(x^{2} + 1) (28 x^{2} + (- x^{2} - 1) \cdot 7)$

Step 8

Apply the distributive property.

(x^{2} + 1) (28 x^{2} - x^{2} \cdot 7 - 1 \cdot 7)

$(x^{2} + 1) (28 x^{2} - x^{2} \cdot 7 - 1 \cdot 7)$

Step 9

Multiply

7

$7$ by

- 1

$- 1$ .

(x^{2} + 1) (28 x^{2} - 7 x^{2} - 1 \cdot 7)

$(x^{2} + 1) (28 x^{2} - 7 x^{2} - 1 \cdot 7)$

Step 10

Multiply

- 1

$- 1$ by

7

$7$ .

(x^{2} + 1) (28 x^{2} - 7 x^{2} - 7)

$(x^{2} + 1) (28 x^{2} - 7 x^{2} - 7)$

Step 11

Subtract

7 x^{2}

$7 x^{2}$ from

28 x^{2}

$28 x^{2}$ .

(x^{2} + 1) (21 x^{2} - 7)

$(x^{2} + 1) (21 x^{2} - 7)$

Step 12

Factor.

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Step 12.1

Factor

7

$7$ out of

21 x^{2} - 7

$21 x^{2} - 7$ .

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Step 12.1.1

Factor

7

$7$ out of

21 x^{2}

$21 x^{2}$ .

(x^{2} + 1) (7 (3 x^{2}) - 7)

$(x^{2} + 1) (7 (3 x^{2}) - 7)$

Step 12.1.2

Factor

7

$7$ out of

- 7

$- 7$ .

(x^{2} + 1) (7 (3 x^{2}) + 7 (- 1))

$(x^{2} + 1) (7 (3 x^{2}) + 7 (- 1))$

Step 12.1.3

Factor

7

$7$ out of

7 (3 x^{2}) + 7 (- 1)

$7 (3 x^{2}) + 7 (- 1)$ .

(x^{2} + 1) (7 (3 x^{2} - 1))

$(x^{2} + 1) (7 (3 x^{2} - 1))$

(x^{2} + 1) (7 (3 x^{2} - 1))

$(x^{2} + 1) (7 (3 x^{2} - 1))$

Step 12.2

Remove unnecessary parentheses.

(x^{2} + 1) \cdot 7 (3 x^{2} - 1)

$(x^{2} + 1) \cdot 7 (3 x^{2} - 1)$

(x^{2} + 1) \cdot 7 (3 x^{2} - 1)

$(x^{2} + 1) \cdot 7 (3 x^{2} - 1)$