The value of `(0.98)^(3) + (0.02)^(3) + 3 xx 0.98 xx 0.02 - 1` is :

Options

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

Answer

To solve the expression \( (0.98)^3 + (0.02)^3 + 3 \times 0.98 \times 0.02 - 1 \), we can use the algebraic identity for the sum of cubes. The identity states that:

\[ A^3 + B^3 + 3AB = (A + B)^3 \]

In our case, let \( A = 0.98 \) and \( B = 0.02 \).

### Step 1: Identify A and B
Let:
- \( A = 0.98 \)
- \( B = 0.02 \)

### Step 2: Apply the identity
According to the identity, we can rewrite the expression:

\[ (0.98)^3 + (0.02)^3 + 3 \times 0.98 \times 0.02 = (0.98 + 0.02)^3 \]

### Step 3: Simplify \( A + B \)
Now, calculate \( A + B \):

\[ A + B = 0.98 + 0.02 = 1 \]

### Step 4: Substitute back into the identity
Substituting back into the identity gives us:

\[ (0.98 + 0.02)^3 = 1^3 = 1 \]

### Step 5: Complete the expression
Now, we need to include the remaining part of the original expression:

\[ 1 - 1 = 0 \]

### Final Answer
Thus, the value of the expression \( (0.98)^3 + (0.02)^3 + 3 \times 0.98 \times 0.02 - 1 \) is:

\[ \boxed{0} \]