Trigonometry Examples

$\frac{4 + v ({(- 4)}^{2} - 4 \cdot 2 \cdot 3)}{2 (2)}$

Step 1

Simplify the numerator.

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$\frac{4 + v (16 - 4 \cdot 2 \cdot 3)}{2 (2)}$

Step 1.1.2

Multiply $- 4 \cdot 2 \cdot 3$ .

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Step 1.1.2.1

Multiply $- 4$ by $2$ .

$\frac{4 + v (16 - 8 \cdot 3)}{2 (2)}$

Step 1.1.2.2

Multiply $- 8$ by $3$ .

$\frac{4 + v (16 - 24)}{2 (2)}$

Step 1.2

Subtract $24$ from $16$ .

$\frac{4 + v \cdot - 8}{2 (2)}$

Step 1.3

Move $- 8$ to the left of $v$ .

$\frac{4 - 8 \cdot v}{2 (2)}$

Step 1.4

Factor $4$ out of $4 - 8 v$ .

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Step 1.4.1

Factor $4$ out of $4$ .

$\frac{4 (1) - 8 v}{2 (2)}$

Step 1.4.2

Factor $4$ out of $- 8 v$ .

$\frac{4 (1) + 4 (- 2 v)}{2 (2)}$

Step 1.4.3

Factor $4$ out of $4 (1) + 4 (- 2 v)$ .

$\frac{4 (1 - 2 v)}{2 (2)}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Multiply $2$ by $2$ .

$\frac{4 (1 - 2 v)}{4}$

Step 2.2

Cancel the common factor of $4$ .

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Step 2.2.1

Cancel the common factor.

$\frac{4 (1 - 2 v)}{4}$

Step 2.2.2

Divide $1 - 2 v$ by $1$ .

$1 - 2 v$