Simplify (1+1/3)^2-2/9

${(1 + \frac{1}{3})}^{2} - \frac{2}{9}$

Simplify each term.

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

${(\frac{3}{3} + \frac{1}{3})}^{2} - \frac{2}{9}$

Combine the numerators over the common denominator.

${(\frac{3 + 1}{3})}^{2} - \frac{2}{9}$

Add $3$ and $1$ .

${(\frac{4}{3})}^{2} - \frac{2}{9}$

Apply the product rule to $\frac{4}{3}$ .

$\frac{4^{2}}{3^{2}} - \frac{2}{9}$

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

$\frac{16}{3^{2}} - \frac{2}{9}$

Raise $3$ to the power of $2$ .

$\frac{16}{9} - \frac{2}{9}$

Combine fractions.

Combine the numerators over the common denominator.

$\frac{16 - 2}{9}$

Subtract $2$ from $16$ .

$\frac{14}{9}$

The result can be shown in multiple forms.

Exact Form:

$\frac{14}{9}$

Decimal Form:

$1.\overline{5}$

Mixed Number Form:

$1 \frac{5}{9}$