Trigonometry Examples

${(\frac{24}{25})}^{2} - {(- \frac{7}{25})}^{2}$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $\frac{24}{25}$ .

$\frac{24^{2}}{25^{2}} - {(- \frac{7}{25})}^{2}$

Step 1.2

Raise $24$ to the power of $2$ .

$\frac{576}{25^{2}} - {(- \frac{7}{25})}^{2}$

Step 1.3

Raise $25$ to the power of $2$ .

$\frac{576}{625} - {(- \frac{7}{25})}^{2}$

Step 1.4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.4.1

Apply the product rule to $- \frac{7}{25}$ .

$\frac{576}{625} - ({(- 1)}^{2} {(\frac{7}{25})}^{2})$

Step 1.4.2

Apply the product rule to $\frac{7}{25}$ .

$\frac{576}{625} - ({(- 1)}^{2} \frac{7^{2}}{25^{2}})$

Step 1.5

Multiply $- 1$ by ${(- 1)}^{2}$ by adding the exponents.

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Step 1.5.1

Move ${(- 1)}^{2}$ .

$\frac{576}{625} + {(- 1)}^{2} \cdot - 1 \frac{7^{2}}{25^{2}}$

Step 1.5.2

Multiply ${(- 1)}^{2}$ by $- 1$ .

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Step 1.5.2.1

Raise $- 1$ to the power of $1$ .

$\frac{576}{625} + {(- 1)}^{2} \cdot {(- 1)}^{1} \frac{7^{2}}{25^{2}}$

Step 1.5.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{576}{625} + {(- 1)}^{2 + 1} \frac{7^{2}}{25^{2}}$

Step 1.5.3

Add $2$ and $1$ .

$\frac{576}{625} + {(- 1)}^{3} \frac{7^{2}}{25^{2}}$

Step 1.6

Raise $- 1$ to the power of $3$ .

$\frac{576}{625} - \frac{7^{2}}{25^{2}}$

Step 1.7

Raise $7$ to the power of $2$ .

$\frac{576}{625} - \frac{49}{25^{2}}$

Step 1.8

Raise $25$ to the power of $2$ .

$\frac{576}{625} - \frac{49}{625}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{576 - 49}{625}$

Step 2.2

Subtract $49$ from $576$ .

$\frac{527}{625}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{527}{625}$

Decimal Form:

$0.8432$