`9997xx10003=?`

Options

A. a) 9999991
B. b) 99999911
C. c) 99999991
D. d) 9999911

Answer

To solve the problem \(9997 \times 10003\), we can use the difference of squares formula. Here’s a step-by-step breakdown of the solution:

### Step 1: Recognize the Numbers
We can rewrite the expression as:
\[ 9997 \times 10003 = (10000 - 3)(10000 + 3) \]
This is useful because it allows us to use the difference of squares formula.

**Hint:** Look for ways to express the numbers in a form that allows you to use algebraic identities.

### Step 2: Apply the Difference of Squares Formula
Using the difference of squares identity:
\[ a^2 - b^2 = (a - b)(a + b) \]
we can set \(a = 10000\) and \(b = 3\). Therefore:
\[ 9997 \times 10003 = 10000^2 - 3^2 \]

**Hint:** Remember the formula \(a^2 - b^2\) can simplify multiplication problems significantly.

### Step 3: Calculate \(10000^2\) and \(3^2\)
Now we calculate:
\[ 10000^2 = 100000000 \]
\[ 3^2 = 9 \]

**Hint:** Squaring a number with zeros can be simplified by counting the zeros.

### Step 4: Subtract the Squares
Now, we subtract the two results:
\[ 100000000 - 9 = 99999991 \]

**Hint:** When subtracting, be careful with borrowing if necessary.

### Final Answer
Thus, the value of \(9997 \times 10003\) is:
\[ \boxed{99999991} \]