`107xx107+93xx93=?`

Options

A. 19578
B. 19418
C. 20098
D. 21908

Explanation

To solve the question \( 107 \times 107 + 93 \times 93 \), we can follow these steps:

### Step 1: Recognize the squares
We can rewrite the expression using squares:
\[ 107 \times 107 = 107^2 \]
\[ 93 \times 93 = 93^2 \]
So, the expression becomes:
\[ 107^2 + 93^2 \]

### Step 2: Use the algebraic identity
We can use the identity:
\[ A^2 + B^2 = (A + B)^2 - 2AB \]
However, in this case, we can also use the identity for the sum of squares:
\[ A^2 + B^2 = (A + B)^2 - 2AB \]
Where \( A = 107 \) and \( B = 93 \).

### Step 3: Calculate \( A + B \) and \( A - B \)
Calculate:
\[ A + B = 107 + 93 = 200 \]
\[ A - B = 107 - 93 = 14 \]

### Step 4: Apply the identity
Using the identity:
\[ 107^2 + 93^2 = (107 + 93)^2 - 2 \times 107 \times 93 \]
Substituting the values:
\[ = 200^2 - 2 \times 107 \times 93 \]

### Step 5: Calculate \( 200^2 \)
Calculate:
\[ 200^2 = 40000 \]

### Step 6: Calculate \( 2 \times 107 \times 93 \)
First, calculate \( 107 \times 93 \):
\[ 107 \times 93 = 9951 \]
Now, multiply by 2:
\[ 2 \times 9951 = 19902 \]

### Step 7: Substitute back into the equation
Now substitute back:
\[ 107^2 + 93^2 = 40000 - 19902 \]

### Step 8: Final calculation
Calculate:
\[ 40000 - 19902 = 20098 \]

### Final Answer
Thus, the answer is:
\[ \boxed{20098} \]

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