Use identities to evaluate: `(502)^(2)`

Answer

To evaluate \( (502)^2 \) using identities, we can follow these steps:

### Step 1: Rewrite the expression
We can express \( 502 \) as \( 500 + 2 \). Thus, we have:
\[ (502)^2 = (500 + 2)^2 \]

### Step 2: Apply the identity
We will use the algebraic identity for the square of a binomial:
\[ (a + b)^2 = a^2 + 2ab + b^2 \]
Here, let \( a = 500 \) and \( b = 2 \). Applying the identity, we get:
\[ (500 + 2)^2 = 500^2 + 2 \cdot 500 \cdot 2 + 2^2 \]

### Step 3: Calculate each term
Now, we will calculate each term separately:
1. \( 500^2 = 250000 \)
2. \( 2 \cdot 500 \cdot 2 = 2000 \)
3. \( 2^2 = 4 \)

### Step 4: Add all the terms together
Now, we sum all the calculated terms:
\[ 250000 + 2000 + 4 = 252004 \]

### Final Result
Thus, the value of \( (502)^2 \) is:
\[ \boxed{252004} \]

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