Find the value of :
`(0.98)^3+(0.02)^3 + 3xx 0.98 xx 0.02-1`

Options

A. 1.98
B. 1.09
C. 1
D. 0

Answer

To solve the expression \( (0.98)^3 + (0.02)^3 + 3 \times 0.98 \times 0.02 - 1 \), we can recognize that it resembles the expansion of a cube.

### Step-by-step solution:

1. **Identify the terms**: The expression consists of three parts:
- \( (0.98)^3 \)
- \( (0.02)^3 \)
- \( 3 \times 0.98 \times 0.02 \)

2. **Recognize the formula**: The expression can be recognized as the expansion of \( a^3 + b^3 + 3ab(a + b) \), where:
- \( a = 0.98 \)
- \( b = 0.02 \)

3. **Apply the formula**: According to the formula, we can rewrite the expression as:
\[ (a + b)^3 - 1 \]
Here, \( a + b = 0.98 + 0.02 = 1 \).

4. **Calculate \( (a + b)^3 \)**:
\[ (1)^3 = 1 \]

5. **Subtract 1**: Now, substituting back into the expression:
\[ 1 - 1 = 0 \]

Thus, the value of the expression \( (0.98)^3 + (0.02)^3 + 3 \times 0.98 \times 0.02 - 1 \) is \( 0 \).

### Final Answer:
\[ \text{The value is } 0. \]