simplify 42 `xx` 48 = ?

Answer

To simplify \( 42 \times 48 \), we can use the difference of squares formula. Here’s the step-by-step solution:

### Step 1: Rewrite the numbers
We can express \( 42 \) and \( 48 \) in a way that makes it easier to apply the difference of squares formula:
\[ 42 = 45 - 3 \quad \text{and} \quad 48 = 45 + 3 \]

### Step 2: Apply the difference of squares formula
The difference of squares formula states that:
\[ (a - b)(a + b) = a^2 - b^2 \]
In our case, we can let \( a = 45 \) and \( b = 3 \). Therefore, we can rewrite our expression as:
\[ (45 - 3)(45 + 3) = 45^2 - 3^2 \]

### Step 3: Calculate \( a^2 \) and \( b^2 \)
Now we calculate \( 45^2 \) and \( 3^2 \):
\[ 45^2 = 2025 \]
\[ 3^2 = 9 \]

### Step 4: Substitute back into the equation
Now we substitute these values back into the equation:
\[ 45^2 - 3^2 = 2025 - 9 \]

### Step 5: Perform the subtraction
Finally, we perform the subtraction:
\[ 2025 - 9 = 2016 \]

### Final Answer
Thus, the simplified result of \( 42 \times 48 \) is:
\[ \boxed{2016} \]