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 problem \(\frac{(0.03)^2 - (0.01)^2}{0.03 - 0.01}\), we can apply the difference of squares formula. Here’s a step-by-step solution:

### Step 1: Identify the formula
The expression \((a^2 - b^2)\) can be factored using the difference of squares formula:
\[ a^2 - b^2 = (a + b)(a - b) \]
In this case, let \(a = 0.03\) and \(b = 0.01\).

### Step 2: Apply the formula
Using the difference of squares formula, we can rewrite the numerator:
\[ (0.03)^2 - (0.01)^2 = (0.03 + 0.01)(0.03 - 0.01) \]

### Step 3: Substitute back into the expression
Now substitute this back into the original expression:
\[ \frac{(0.03 + 0.01)(0.03 - 0.01)}{0.03 - 0.01} \]

### Step 4: Simplify the expression
Notice that \(0.03 - 0.01\) in the numerator and denominator will cancel out:
\[ = 0.03 + 0.01 \]

### Step 5: Calculate the final value
Now, we can simply add \(0.03\) and \(0.01\):
\[ 0.03 + 0.01 = 0.04 \]

Thus, the value of the expression is:
\[ \boxed{0.04} \]