Using suitable identity evaluate the
`47 xx 53`

Options

A. 2490
B. 2491
C. 2492
D. 2493

Answer

To evaluate \( 47 \times 53 \) using a suitable identity, we can follow these steps:

### Step 1: Rewrite the numbers
We can express \( 47 \) and \( 53 \) in terms of a number close to them. Here, we can write:
\[ 47 = 50 - 3 \quad \text{and} \quad 53 = 50 + 3 \]

### Step 2: Identify the identity
We can use the algebraic identity:
\[ (a - b)(a + b) = a^2 - b^2 \]
In our case, let \( a = 50 \) and \( b = 3 \).

### Step 3: Apply the identity
Now, substituting \( a \) and \( b \) into the identity, we have:
\[ (50 - 3)(50 + 3) = 50^2 - 3^2 \]

### Step 4: Calculate \( a^2 \) and \( b^2 \)
Now, we calculate \( 50^2 \) and \( 3^2 \):
\[ 50^2 = 2500 \]
\[ 3^2 = 9 \]

### Step 5: Subtract \( b^2 \) from \( a^2 \)
Now, we subtract \( 3^2 \) from \( 50^2 \):
\[ 50^2 - 3^2 = 2500 - 9 = 2491 \]

### Final Answer
Thus, the value of \( 47 \times 53 \) is:
\[ \boxed{2491} \]

---