Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

$\frac{49}{25^{2}} - {(\frac{24}{25})}^{2}$

Step 1.3

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

$\frac{49}{625} - {(\frac{24}{25})}^{2}$

Step 1.4

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

$\frac{49}{625} - \frac{24^{2}}{25^{2}}$

Step 1.5

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

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

Step 1.6

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

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

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

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

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

Step 2.2

Simplify the expression.

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Step 2.2.1

Subtract $576$ from $49$ .

$\frac{- 527}{625}$

Step 2.2.2

Move the negative in front of the fraction.

$- \frac{527}{625}$

$- \frac{527}{625}$

$- \frac{527}{625}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{527}{625}$

Decimal Form:

$- 0.8432$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$