Evaluate 2(4/5)^2-1

$2 {(\frac{4}{5})}^{2} - 1$

Step 1

Simplify each term.

Apply the product rule to $\frac{4}{5}$ .

$2 \frac{4^{2}}{5^{2}} - 1$

Raise $4$ to the power of $2$ .

$2 \frac{16}{5^{2}} - 1$

Raise $5$ to the power of $2$ .

$2 (\frac{16}{25}) - 1$

Multiply $2 (\frac{16}{25})$ .

Combine $2$ and $\frac{16}{25}$ .

$\frac{2 \cdot 16}{25} - 1$

Multiply $2$ by $16$ .

$\frac{32}{25} - 1$

Step 2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$\frac{32}{25} - 1 \cdot \frac{25}{25}$

Step 3

Combine $- 1$ and $\frac{25}{25}$ .

$\frac{32}{25} + \frac{- 1 \cdot 25}{25}$

Step 4

Combine the numerators over the common denominator.

$\frac{32 - 1 \cdot 25}{25}$

Step 5

Simplify the numerator.

Multiply $- 1$ by $25$ .

$\frac{32 - 25}{25}$

Subtract $25$ from $32$ .

$\frac{7}{25}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{25}$

Decimal Form:

$0.28$