Algebra Examples

${(- \frac{8}{17})}^{2} - {(\frac{15}{17})}^{2}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Apply the product rule to $- \frac{8}{17}$ .

${(- 1)}^{2} {(\frac{8}{17})}^{2} - {(\frac{15}{17})}^{2}$

Step 1.1.2

Apply the product rule to $\frac{8}{17}$ .

${(- 1)}^{2} \frac{8^{2}}{17^{2}} - {(\frac{15}{17})}^{2}$

Step 1.2

Raise $- 1$ to the power of $2$ .

$1 \frac{8^{2}}{17^{2}} - {(\frac{15}{17})}^{2}$

Step 1.3

Multiply $\frac{8^{2}}{17^{2}}$ by $1$ .

$\frac{8^{2}}{17^{2}} - {(\frac{15}{17})}^{2}$

Step 1.4

Raise $8$ to the power of $2$ .

$\frac{64}{17^{2}} - {(\frac{15}{17})}^{2}$

Step 1.5

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

$\frac{64}{289} - {(\frac{15}{17})}^{2}$

Step 1.6

Apply the product rule to $\frac{15}{17}$ .

$\frac{64}{289} - \frac{15^{2}}{17^{2}}$

Step 1.7

Raise $15$ to the power of $2$ .

$\frac{64}{289} - \frac{225}{17^{2}}$

Step 1.8

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

$\frac{64}{289} - \frac{225}{289}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{64 - 225}{289}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Subtract $225$ from $64$ .

$\frac{- 161}{289}$

Step 2.2.2

Move the negative in front of the fraction.

$- \frac{161}{289}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{161}{289}$

Decimal Form:

$- 0.55709342 \dots$