Find the value of question mark (?) in the following questions given below
`(185)^(2)`

Options

A. 34,225
B. 370
C. 22,225
D. 270

Answer

To find the value of \( 185^2 \), we can use the formula for the square of a binomial. The formula states:

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

In this case, we can express \( 185 \) as \( 200 - 15 \). Here, \( a = 200 \) and \( b = 15 \). Now, we can apply the formula step by step.

### Step 1: Identify \( a \) and \( b \)
Let:
- \( a = 200 \)
- \( b = 15 \)

### Step 2: Apply the formula
Using the formula \( (a - b)^2 = a^2 - 2ab + b^2 \):

\[ 185^2 = (200 - 15)^2 = 200^2 - 2 \cdot 200 \cdot 15 + 15^2 \]

### Step 3: Calculate \( a^2 \)
Calculate \( 200^2 \):

\[ 200^2 = 40000 \]

### Step 4: Calculate \( 2ab \)
Calculate \( 2 \cdot 200 \cdot 15 \):

\[ 2 \cdot 200 \cdot 15 = 6000 \]

### Step 5: Calculate \( b^2 \)
Calculate \( 15^2 \):

\[ 15^2 = 225 \]

### Step 6: Substitute the values back into the equation
Now substitute these values back into the equation:

\[ 185^2 = 40000 - 6000 + 225 \]

### Step 7: Perform the arithmetic
Now, simplify the expression:

\[ 40000 - 6000 = 34000 \]
\[ 34000 + 225 = 34225 \]

Thus, the value of \( 185^2 \) is:

\[ 185^2 = 34225 \]

### Final Answer
The value of the question mark (?) is **34,225**.

---