105 × 105 = ?

Options

A. (a) 10500
B. (b) 11250
C. (c) 11520
D. (d) 11025

Answer

To solve the problem \( 105 \times 105 \), we can use the formula for the square of a binomial. Here’s a step-by-step breakdown of the solution:

### Step 1: Rewrite the Expression
We start with the expression:
\[ 105 \times 105 \]
This can be rewritten as:
\[ 105^2 \]

### Step 2: Use the Binomial Expansion
Next, we can express \( 105 \) as \( 100 + 5 \):
\[ 105^2 = (100 + 5)^2 \]
Now, we can apply the binomial expansion formula \( (a + b)^2 = a^2 + 2ab + b^2 \), where \( a = 100 \) and \( b = 5 \).

### Step 3: Calculate Each Term
Now we calculate each term:
- \( a^2 = 100^2 = 10,000 \)
- \( b^2 = 5^2 = 25 \)
- \( 2ab = 2 \times 100 \times 5 = 1,000 \)

### Step 4: Combine the Results
Now, we combine all the terms:
\[ 105^2 = 10,000 + 1,000 + 25 \]
Calculating this gives:
\[ 10,000 + 1,000 = 11,000 \]
Then adding \( 25 \):
\[ 11,000 + 25 = 11,025 \]

### Final Answer
Thus, the value of \( 105 \times 105 \) is:
\[ \boxed{11025} \]

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