Trigonometry Examples

$v ({(3957 + \frac{400}{5280})}^{2} - {(3957)}^{2})$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $400$ and $5280$ .

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Step 1.1.1

Factor $80$ out of $400$ .

$v ({(3957 + \frac{80 (5)}{5280})}^{2} - {(3957)}^{2})$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $80$ out of $5280$ .

$v ({(3957 + \frac{80 \cdot 5}{80 \cdot 66})}^{2} - {(3957)}^{2})$

Step 1.1.2.2

Cancel the common factor.

$v ({(3957 + \frac{80 \cdot 5}{80 \cdot 66})}^{2} - {(3957)}^{2})$

Step 1.1.2.3

Rewrite the expression.

$v ({(3957 + \frac{5}{66})}^{2} - {(3957)}^{2})$

Step 1.2

To write $3957$ as a fraction with a common denominator, multiply by $\frac{66}{66}$ .

$v ({(3957 \cdot \frac{66}{66} + \frac{5}{66})}^{2} - {(3957)}^{2})$

Step 1.3

Combine $3957$ and $\frac{66}{66}$ .

$v ({(\frac{3957 \cdot 66}{66} + \frac{5}{66})}^{2} - {(3957)}^{2})$

Step 1.4

Combine the numerators over the common denominator.

$v ({(\frac{3957 \cdot 66 + 5}{66})}^{2} - {(3957)}^{2})$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $3957$ by $66$ .

$v ({(\frac{261162 + 5}{66})}^{2} - {(3957)}^{2})$

Step 1.5.2

Add $261162$ and $5$ .

$v ({(\frac{261167}{66})}^{2} - {(3957)}^{2})$

Step 1.6

Apply the product rule to $\frac{261167}{66}$ .

$v (\frac{261167^{2}}{66^{2}} - {(3957)}^{2})$

Step 1.7

Raise $261167$ to the power of $2$ .

$v (\frac{68208201889}{66^{2}} - {(3957)}^{2})$

Step 1.8

Raise $66$ to the power of $2$ .

$v (\frac{68208201889}{4356} - {(3957)}^{2})$

Step 1.9

Raise $3957$ to the power of $2$ .

$v (\frac{68208201889}{4356} - 1 \cdot 15657849)$

Step 1.10

Multiply $- 1$ by $15657849$ .

$v (\frac{68208201889}{4356} - 15657849)$

Step 2

To write $- 15657849$ as a fraction with a common denominator, multiply by $\frac{4356}{4356}$ .

$v (\frac{68208201889}{4356} - 15657849 \cdot \frac{4356}{4356})$

Step 3

Combine $- 15657849$ and $\frac{4356}{4356}$ .

$v (\frac{68208201889}{4356} + \frac{- 15657849 \cdot 4356}{4356})$

Step 4

Combine the numerators over the common denominator.

$v \frac{68208201889 - 15657849 \cdot 4356}{4356}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 15657849$ by $4356$ .

$v \frac{68208201889 - 68205590244}{4356}$

Step 5.2

Subtract $68205590244$ from $68208201889$ .

$v \frac{2611645}{4356}$

Step 6

Combine $v$ and $\frac{2611645}{4356}$ .

$\frac{v \cdot 2611645}{4356}$

Step 7

Move $2611645$ to the left of $v$ .

$\frac{2611645 v}{4356}$