Trigonometry Examples

$v ((17^{2}) - ({(4 \sqrt{17})}^{2}))$

Step 1

Simplify each term.

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Step 1.1

Raise $17$ to the power of $2$ .

$v (289 - ({(4 \sqrt{17})}^{2}))$

Step 1.2

Apply the product rule to $4 \sqrt{17}$ .

$v (289 - (4^{2} {\sqrt{17}}^{2}))$

Step 1.3

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

$v (289 - (16 {\sqrt{17}}^{2}))$

Step 1.4

Rewrite ${\sqrt{17}}^{2}$ as $17$ .

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Step 1.4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{17}$ as $17^{\frac{1}{2}}$ .

$v (289 - (16 {(17^{\frac{1}{2}})}^{2}))$

Step 1.4.2

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

$v (289 - (16 \cdot 17^{\frac{1}{2} \cdot 2}))$

Step 1.4.3

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

$v (289 - (16 \cdot 17^{\frac{2}{2}}))$

Step 1.4.4

Cancel the common factor of $2$ .

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Step 1.4.4.1

Cancel the common factor.

$v (289 - (16 \cdot 17^{\frac{2}{2}}))$

Step 1.4.4.2

Rewrite the expression.

$v (289 - (16 \cdot 17^{1}))$

Step 1.4.5

Evaluate the exponent.

$v (289 - (16 \cdot 17))$

Step 1.5

Multiply $- (16 \cdot 17)$ .

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Step 1.5.1

Multiply $16$ by $17$ .

$v (289 - 1 \cdot 272)$

Step 1.5.2

Multiply $- 1$ by $272$ .

$v (289 - 272)$

Step 2

Simplify the expression.

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Step 2.1

Subtract $272$ from $289$ .

$v \cdot 17$

Step 2.2

Move $17$ to the left of $v$ .

$17 v$