Which of the following is a quadratic equation?

Options

A. `x^(2)+2x+1=(4-x)^(2)+3`
B. `-2x^(2)=(5-x)(2x-2/5)`
C. `(k+1)x^(2)+3/2x=7`, where `k=-1`
D. `x^(3)-x^(2)=(x-1)^(3)`

Explanation

To determine which of the given options is a quadratic equation, we need to check each equation against the standard form of a quadratic equation, which is:

\[ ax^2 + bx + c = 0 \]

where \( a \neq 0 \).

### Step-by-Step Solution:

1. **Option A: \( x^2 + 2x + 1 = 4 - x^2 \)**
- Rearranging gives:
\[ x^2 + 2x + 1 + x^2 - 4 = 0 \]
\[ 2x^2 + 2x - 3 = 0 \]
- Here, the coefficient of \( x^2 \) is 2 (not zero), so this is a quadratic equation.

2. **Option B: \( -2x^2 = 10x - 5 \)**
- Rearranging gives:
\[ -2x^2 - 10x + 5 = 0 \]
- Here, the coefficient of \( x^2 \) is -2 (not zero), so this is a quadratic equation.

3. **Option C: \( k = -1 \) leads to \( -1 + 1 \cdot x^2 + \frac{3}{2}x = 7 \)**
- Rearranging gives:
\[ x^2 + \frac{3}{2}x - 8 = 0 \]
- Here, the coefficient of \( x^2 \) is 1 (not zero), so this is a quadratic equation.

4. **Option D: \( x^3 - x^2 = a - b^3 \)**
- Rearranging gives:
\[ x^3 - x^2 - (a - b^3) = 0 \]
- This equation has a term \( x^3 \), which indicates that it is not a quadratic equation since the highest power of \( x \) is 3.

### Conclusion:
The quadratic equations among the options are A, B, and C. However, Option D is not a quadratic equation.

### Final Answer:
The correct answer is **Option D** is not a quadratic equation.