Simplify: `(3.6+6.4) (3.6-6.4) - (3.6-6.4)^(2)`= ?

Options

A. `29.6`
B. `32.6`
C. `32.68`
D. `-35.84`

Answer

To simplify the expression `(3.6 + 6.4)(3.6 - 6.4) - (3.6 - 6.4)²`, we can follow these steps:

### Step 1: Identify the components of the expression
We have two parts in the expression:
1. `(3.6 + 6.4)(3.6 - 6.4)`
2. `(3.6 - 6.4)²`

### Step 2: Calculate `3.6 + 6.4` and `3.6 - 6.4`
- `3.6 + 6.4 = 10`
- `3.6 - 6.4 = -2.8`

### Step 3: Substitute the values into the expression
Now we can substitute these values back into the expression:
- The expression becomes: `(10)(-2.8) - (-2.8)²`

### Step 4: Calculate the first part `(10)(-2.8)`
- `10 * -2.8 = -28`

### Step 5: Calculate the second part `(-2.8)²`
- `(-2.8)² = 7.84`

### Step 6: Substitute back into the expression
Now we have:
- `-28 - 7.84`

### Step 7: Perform the final calculation
- `-28 - 7.84 = -35.84`

### Final Answer
Thus, the simplified expression is:
- **Answer: -35.84**

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