Find the values of the following by using suitable identity:
`(26)^(2)`

Answer

To find the value of \( (26)^2 \) using a suitable identity, we can follow these steps:

### Step 1: Rewrite 26
We can express \( 26 \) as \( 25 + 1 \).

### Step 2: Use the Identity
We will use the identity for the square of a binomial:
\[ (a + b)^2 = a^2 + 2ab + b^2 \]
Here, let \( a = 25 \) and \( b = 1 \).

### Step 3: Substitute Values into the Identity
Now, substituting \( a \) and \( b \) into the identity:
\[ (25 + 1)^2 = 25^2 + 2 \cdot 25 \cdot 1 + 1^2 \]

### Step 4: Calculate Each Term
Now we calculate each term:
- \( 25^2 = 625 \)
- \( 2 \cdot 25 \cdot 1 = 50 \)
- \( 1^2 = 1 \)

### Step 5: Add the Results
Now, we add these results together:
\[ 625 + 50 + 1 = 676 \]

### Conclusion
Thus, the value of \( (26)^2 \) is \( 676 \).

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