Trigonometry Examples

$v (- 3^{2} + {(- 3 \sqrt{3})}^{2})$

Step 1

Simplify each term.

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Step 1.1

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

$v (- 1 \cdot 9 + {(- 3 \sqrt{3})}^{2})$

Step 1.2

Multiply $- 1$ by $9$ .

$v (- 9 + {(- 3 \sqrt{3})}^{2})$

Step 1.3

Apply the product rule to $- 3 \sqrt{3}$ .

$v (- 9 + {(- 3)}^{2} {\sqrt{3}}^{2})$

Step 1.4

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

$v (- 9 + 9 {\sqrt{3}}^{2})$

Step 1.5

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 1.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$v (- 9 + 9 {(3^{\frac{1}{2}})}^{2})$

Step 1.5.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$v (- 9 + 9 \cdot 3^{\frac{1}{2} \cdot 2})$

Step 1.5.3

Combine $\frac{1}{2}$ and $2$ .

$v (- 9 + 9 \cdot 3^{\frac{2}{2}})$

Step 1.5.4

Cancel the common factor of $2$ .

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Step 1.5.4.1

Cancel the common factor.

$v (- 9 + 9 \cdot 3^{\frac{2}{2}})$

Step 1.5.4.2

Rewrite the expression.

$v (- 9 + 9 \cdot 3^{1})$

Step 1.5.5

Evaluate the exponent.

$v (- 9 + 9 \cdot 3)$

Step 1.6

Multiply $9$ by $3$ .

$v (- 9 + 27)$

Step 2

Simplify the expression.

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Step 2.1

Add $- 9$ and $27$ .

$v \cdot 18$

Step 2.2

Move $18$ to the left of $v$ .

$18 v$