`75^(2)` =?

Options

A. 5625
B. 5645
C. 5525
D. 5555

Answer

To solve the problem \( 75^2 \), we can use the formula for the square of a binomial, which states that:

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

In this case, we can express \( 75 \) as \( 50 + 25 \). Thus, we have:

\[ 75^2 = (50 + 25)^2 \]

Now, we can apply the binomial square formula:

1. **Identify \( a \) and \( b \)**:
- Let \( a = 50 \)
- Let \( b = 25 \)

2. **Calculate \( a^2 \)**:
\[ a^2 = 50^2 = 2500 \]

3. **Calculate \( b^2 \)**:
\[ b^2 = 25^2 = 625 \]

4. **Calculate \( 2ab \)**:
\[ 2ab = 2 \times 50 \times 25 = 2 \times 1250 = 2500 \]

5. **Combine all the parts**:
\[ 75^2 = a^2 + b^2 + 2ab = 2500 + 625 + 2500 \]

6. **Add the values together**:
\[ 2500 + 625 = 3125 \]
\[ 3125 + 2500 = 5625 \]

Thus, the final answer is:

\[ 75^2 = 5625 \]