`(5.5)^(3) - (4.5)^(3)` is equal to :

Options

A. A) 1
B. B) 75
C. C) 74.25
D. D) 75.25

Answer

To solve the expression \( (5.5)^3 - (4.5)^3 \), we can utilize the formula for the difference of cubes, which states:

\[ A^3 - B^3 = (A - B)(A^2 + AB + B^2) \]

Here, we can let \( A = 5.5 \) and \( B = 4.5 \).

### Step 1: Calculate \( A - B \)

\[ A - B = 5.5 - 4.5 = 1 \]

### Step 2: Calculate \( A^2 \)

\[ A^2 = (5.5)^2 = 30.25 \]

### Step 3: Calculate \( B^2 \)

\[ B^2 = (4.5)^2 = 20.25 \]

### Step 4: Calculate \( AB \)

\[ AB = 5.5 \times 4.5 = 24.75 \]

### Step 5: Calculate \( A^2 + AB + B^2 \)

Now we can add these values together:

\[ A^2 + AB + B^2 = 30.25 + 24.75 + 20.25 \]

Calculating this step-by-step:

1. \( 30.25 + 24.75 = 55 \)
2. \( 55 + 20.25 = 75.25 \)

### Step 6: Combine the results

Now we substitute back into the difference of cubes formula:

\[ (5.5)^3 - (4.5)^3 = (A - B)(A^2 + AB + B^2) = 1 \times 75.25 = 75.25 \]

### Final Answer

Thus, the value of \( (5.5)^3 - (4.5)^3 \) is:

\[ \boxed{75.25} \]

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