The value of `((0.03)^(2) - (0.01)^(2))/(0.03 - 0.01)` is :

Options

A. 0.02
B. 0.004
C. 0.4
D. 0.04

Answer

To solve the expression \(\frac{(0.03)^2 - (0.01)^2}{0.03 - 0.01}\), we can use the difference of squares formula, which states that \(a^2 - b^2 = (a + b)(a - b)\).

### Step-by-Step Solution:

1. **Identify \(a\) and \(b\)**:
- Let \(a = 0.03\) and \(b = 0.01\).

2. **Apply the difference of squares formula**:
- According to the formula, we can rewrite the expression:
\[ (0.03)^2 - (0.01)^2 = (0.03 + 0.01)(0.03 - 0.01) \]

3. **Calculate \(0.03 + 0.01\)**:
- \(0.03 + 0.01 = 0.04\)

4. **Calculate \(0.03 - 0.01\)**:
- \(0.03 - 0.01 = 0.02\)

5. **Substitute back into the expression**:
- Now, substituting these values back into the expression:
\[ \frac{(0.03 + 0.01)(0.03 - 0.01)}{0.03 - 0.01} = \frac{(0.04)(0.02)}{0.02} \]

6. **Simplify the expression**:
- The \(0.02\) in the numerator and denominator cancels out:
\[ \frac{0.04 \cdot 0.02}{0.02} = 0.04 \]

### Final Answer:
The value of \(\frac{(0.03)^2 - (0.01)^2}{0.03 - 0.01}\) is \(0.04\).

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