Find the product without multiplying directly `106 xx 94`.

Answer

To find the product of \(106\) and \(94\) without multiplying directly, we can use the difference of squares identity. Here’s how we can do it step by step:

### Step 1: Rewrite the numbers
We can express \(106\) and \(94\) in a form that allows us to use the difference of squares identity. We can write:
\[ 106 = 100 + 6 \quad \text{and} \quad 94 = 100 - 6 \]

### Step 2: Apply the difference of squares identity
Using the identity \( (a + b)(a - b) = a^2 - b^2 \), where \(a = 100\) and \(b = 6\), we can rewrite the product:
\[ 106 \times 94 = (100 + 6)(100 - 6) = 100^2 - 6^2 \]

### Step 3: Calculate \(100^2\) and \(6^2\)
Now, we calculate \(100^2\) and \(6^2\):
\[ 100^2 = 10000 \]
\[ 6^2 = 36 \]

### Step 4: Subtract the squares
Now, we substitute these values back into the equation:
\[ 106 \times 94 = 10000 - 36 \]

### Step 5: Perform the subtraction
Finally, we perform the subtraction:
\[ 10000 - 36 = 9964 \]

Thus, the product of \(106\) and \(94\) is:
\[ \boxed{9964} \]

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