Evaluate 1-2(12/13)^2

$1 - 2 {(\frac{12}{13})}^{2}$

Step 1

Simplify each term.

Apply the product rule to $\frac{12}{13}$ .

$1 - 2 \frac{12^{2}}{13^{2}}$

Raise $12$ to the power of $2$ .

$1 - 2 \frac{144}{13^{2}}$

Raise $13$ to the power of $2$ .

$1 - 2 (\frac{144}{169})$

Multiply $- 2 (\frac{144}{169})$ .

Combine $- 2$ and $\frac{144}{169}$ .

$1 + \frac{- 2 \cdot 144}{169}$

Multiply $- 2$ by $144$ .

$1 + \frac{- 288}{169}$

Move the negative in front of the fraction.

$1 - \frac{288}{169}$

Step 2

Simplify the expression.

Write $1$ as a fraction with a common denominator.

$\frac{169}{169} - \frac{288}{169}$

Combine the numerators over the common denominator.

$\frac{169 - 288}{169}$

Subtract $288$ from $169$ .

$\frac{- 119}{169}$

Move the negative in front of the fraction.

$- \frac{119}{169}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{119}{169}$

Decimal Form:

$- 0.70414201 \dots$