Find the square of 112.

Options

A. 12444
B. 12504
C. 12584
D. 12544

Answer

To find the square of 112, we can use the formula for squaring a two-digit number, which is based on the identity:

\[ (a + b)^2 = a^2 + 2ab + b^2 \]

In this case, we can break down 112 into \(100 + 12\).

### Step 1: Identify \(a\) and \(b\)
Let:
- \(a = 100\)
- \(b = 12\)

### Step 2: Calculate \(a^2\)
Calculate \(a^2\):
\[ a^2 = 100^2 = 10000 \]

### Step 3: Calculate \(b^2\)
Calculate \(b^2\):
\[ b^2 = 12^2 = 144 \]

### Step 4: Calculate \(2ab\)
Calculate \(2ab\):
\[ 2ab = 2 \times 100 \times 12 = 2400 \]

### Step 5: Combine the results
Now, combine all the results using the formula:
\[ (100 + 12)^2 = a^2 + 2ab + b^2 \]
\[ = 10000 + 2400 + 144 \]

### Step 6: Perform the addition
Now, add these values together:
\[ 10000 + 2400 = 12400 \]
\[ 12400 + 144 = 12544 \]

Thus, the square of 112 is:
\[ \boxed{12544} \]

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