Basic Math Examples

${(\frac{21}{29})}^{2} - {(- \frac{20}{29})}^{2}$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $\frac{21}{29}$ .

$\frac{21^{2}}{29^{2}} - {(- \frac{20}{29})}^{2}$

Step 1.2

Raise $21$ to the power of $2$ .

$\frac{441}{29^{2}} - {(- \frac{20}{29})}^{2}$

Step 1.3

Raise $29$ to the power of $2$ .

$\frac{441}{841} - {(- \frac{20}{29})}^{2}$

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 $- \frac{20}{29}$ .

$\frac{441}{841} - ({(- 1)}^{2} {(\frac{20}{29})}^{2})$

Step 1.4.2

Apply the product rule to $\frac{20}{29}$ .

$\frac{441}{841} - ({(- 1)}^{2} \frac{20^{2}}{29^{2}})$

Step 1.5

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

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Step 1.5.1

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

$\frac{441}{841} + {(- 1)}^{2} \cdot - 1 \frac{20^{2}}{29^{2}}$

Step 1.5.2

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

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Step 1.5.2.1

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

$\frac{441}{841} + {(- 1)}^{2} \cdot {(- 1)}^{1} \frac{20^{2}}{29^{2}}$

Step 1.5.2.2

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

$\frac{441}{841} + {(- 1)}^{2 + 1} \frac{20^{2}}{29^{2}}$

Step 1.5.3

Add $2$ and $1$ .

$\frac{441}{841} + {(- 1)}^{3} \frac{20^{2}}{29^{2}}$

Step 1.6

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

$\frac{441}{841} - \frac{20^{2}}{29^{2}}$

Step 1.7

Raise $20$ to the power of $2$ .

$\frac{441}{841} - \frac{400}{29^{2}}$

Step 1.8

Raise $29$ to the power of $2$ .

$\frac{441}{841} - \frac{400}{841}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{441 - 400}{841}$

Step 2.2

Subtract $400$ from $441$ .

$\frac{41}{841}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{41}{841}$

Decimal Form:

$0.04875148 \dots$