`2.33xx2.33xx+0.33xx0.33xx-0.66xx2.33` is equal to:

Options

A. 2.66
B. 0.4
C. 4
D. 2

Answer

To solve the expression \( 2.33 \times 2.33 + 0.33 \times 0.33 - 0.66 \times 2.33 \), we can follow these steps:

### Step 1: Rewrite the Expression
We start with the expression:
\[ 2.33 \times 2.33 + 0.33 \times 0.33 - 0.66 \times 2.33 \]

### Step 2: Recognize the Terms
Notice that \( 0.66 \) can be rewritten as \( 2 \times 0.33 \). Thus, we can rewrite the expression as:
\[ 2.33^2 + 0.33^2 - (2 \times 0.33 \times 2.33) \]

### Step 3: Apply the Identity
We can recognize that this expression resembles the expansion of the square of a binomial. The identity we can use is:
\[ (A - B)^2 = A^2 + B^2 - 2AB \]
where \( A = 2.33 \) and \( B = 0.33 \).

### Step 4: Substitute into the Identity
Using the values of \( A \) and \( B \):
\[ (2.33 - 0.33)^2 = 2.33^2 + 0.33^2 - 2 \times 0.33 \times 2.33 \]

### Step 5: Simplify
Now, calculate \( 2.33 - 0.33 \):
\[ 2.33 - 0.33 = 2.00 \]
Thus, we have:
\[ (2.00)^2 = 2.33^2 + 0.33^2 - 0.66 \times 2.33 \]

### Step 6: Calculate the Square
Calculating \( (2.00)^2 \):
\[ (2.00)^2 = 4.00 \]

### Conclusion
The expression simplifies to:
\[ 2.33^2 + 0.33^2 - 0.66 \times 2.33 = 4.00 \]

Thus, the answer is:
\[ \boxed{4} \]