`98^(2)`=?

Options

A. 9604
B. 9640
C. 9654
D. 8684

Answer

To solve the question \( 98^2 \), we can use the formula for the square of a binomial. Here’s the step-by-step solution:

### Step 1: Rewrite \( 98^2 \)
We can express \( 98 \) as \( 100 - 2 \). Therefore, we can rewrite the expression:
\[ 98^2 = (100 - 2)^2 \]

### Step 2: Apply the Binomial Square Formula
Using the formula for the square of a binomial, \( (A - B)^2 = A^2 - 2AB + B^2 \), where \( A = 100 \) and \( B = 2 \):
\[ (100 - 2)^2 = 100^2 - 2 \cdot 100 \cdot 2 + 2^2 \]

### Step 3: Calculate Each Term
Now we calculate each term:
- \( 100^2 = 10000 \)
- \( 2^2 = 4 \)
- \( 2 \cdot 100 \cdot 2 = 400 \)

### Step 4: Substitute Back into the Expression
Substituting these values back into the expression gives us:
\[ 98^2 = 10000 - 400 + 4 \]

### Step 5: Simplify the Expression
Now we simplify:
\[ 98^2 = 10000 + 4 - 400 \]
\[ 98^2 = 10004 - 400 \]
\[ 98^2 = 9604 \]

### Final Answer
Thus, the value of \( 98^2 \) is:
\[ \boxed{9604} \]

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