Use identities to evaluate: `(101)^(2)`

Answer

To evaluate \( (101)^2 \) using the identity, we can follow these steps:

### Step 1: Rewrite the expression
We can express \( 101 \) as \( 100 + 1 \). So, we have:
\[ (101)^2 = (100 + 1)^2 \]

### Step 2: Apply the identity
We will use the identity for the square of a binomial, which states:
\[ (a + b)^2 = a^2 + b^2 + 2ab \]
In our case, \( a = 100 \) and \( b = 1 \). Applying the identity:
\[ (100 + 1)^2 = 100^2 + 1^2 + 2 \cdot 100 \cdot 1 \]

### Step 3: Calculate each term
Now we calculate each term:
1. \( 100^2 = 10000 \)
2. \( 1^2 = 1 \)
3. \( 2 \cdot 100 \cdot 1 = 200 \)

### Step 4: Combine the results
Now, we can combine all the calculated terms:
\[ 10000 + 1 + 200 = 10201 \]

### Final Result
Thus, the value of \( (101)^2 \) is:
\[ \boxed{10201} \]

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