`(cdot 98 xx cdot 98 – cdot 98 xx 1 cdot 52 + cdot 76 xx cdot 76)` = ?

Options

A. `cdot 0484`
B. `cdot 2684`
C. `cdot 3164`
D. `cdot 1562`

Answer

To solve the expression \(0.98 \times 0.98 - 0.98 \times 1.52 + 0.76 \times 0.76\), we can follow these steps:

### Step 1: Rewrite the expression
We start with the original expression:
\[ 0.98 \times 0.98 - 0.98 \times 1.52 + 0.76 \times 0.76 \]

### Step 2: Identify squares
Recognize that \(0.98 \times 0.98\) is the square of \(0.98\) and \(0.76 \times 0.76\) is the square of \(0.76\):
\[ (0.98)^2 - 0.98 \times 1.52 + (0.76)^2 \]

### Step 3: Use the formula for squares
Notice that we can use the identity \(a^2 - 2ab + b^2 = (a - b)^2\). Here, we can express the middle term as:
\[ 0.98 \times 1.52 = 2 \times 0.98 \times 0.76 \]
Thus, the expression can be rewritten as:
\[ (0.98)^2 - 2 \times 0.98 \times 0.76 + (0.76)^2 \]

### Step 4: Apply the square formula
Now we can apply the square formula:
\[ (0.98 - 0.76)^2 \]

### Step 5: Calculate \(0.98 - 0.76\)
Calculate the difference:
\[ 0.98 - 0.76 = 0.22 \]

### Step 6: Square the result
Now square the result:
\[ (0.22)^2 = 0.0484 \]

### Step 7: Final expression
Now, we need to add the values we calculated:
\[ 0.0484 \]

### Conclusion
Thus, the final answer to the expression \(0.98 \times 0.98 - 0.98 \times 1.52 + 0.76 \times 0.76\) is:
\[ \boxed{0.0484} \]