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Simplify:

[tex]\[ \left(1+\frac{1}{3}\right)^2 - \frac{2}{9} \][/tex]

Enter your answer as a simplified fraction in the box.

[tex]\[ \boxed{\square} \][/tex]

Sagot :

GinnyAnsweridn
To simplify the given expression [tex]\(\left(1 + \frac{1}{3}\right)^2 - \frac{2}{9}\)[/tex], follow these steps carefully:

### Step 1: Convert the Mixed Number to an Improper Fraction

First, express the mixed number [tex]\(1 + \frac{1}{3}\)[/tex] as an improper fraction.
[tex]\[ 1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3} \][/tex]

### Step 2: Square the Improper Fraction

Next, square the improper fraction [tex]\(\frac{4}{3}\)[/tex].
[tex]\[ \left(\frac{4}{3}\right)^2 = \frac{4^2}{3^2} = \frac{16}{9} \][/tex]

### Step 3: Subtract the Second Term from the Squared Value

Now, subtract [tex]\(\frac{2}{9}\)[/tex] from [tex]\(\frac{16}{9}\)[/tex].
[tex]\[ \frac{16}{9} - \frac{2}{9} = \frac{16 - 2}{9} = \frac{14}{9} \][/tex]

### Conclusion

So, the expression [tex]\(\left(1 + \frac{1}{3}\right)^2 - \frac{2}{9}\)[/tex] simplifies to [tex]\(\frac{14}{9}\)[/tex].

Therefore, the simplified fraction is:
[tex]\[ \boxed{\frac{14}{9}} \][/tex]
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