The standard form of a quadratic equation is given by,

ax² + bx + c = 0, a ≠ 0

A. Given, x² + 2x + 1 = (4 - x)² + 3

⇒ x² + 2x + 1 = 16 - 8x + x² + 3

∴ 10x – 18 = 0

which is not a quadratic equation.

B. Given, -2x² = (5 - x) (2x – )

⇒ -2x² = 10x - 2x² – 2 +

∴ 52x – 10 = 0

which is not a quadratic equation.

C. Given, (k + 1) x² + = 7, where k = -1

⇒ (-1 + 1) x² + = 7

∴ 3x – 14 = 0

which is not a quadratic equation.

D. Given, x³ - x² = (x - 1)³

⇒ x³ - x² = x³ - 3x² + 3x - 1

∴ 2x² - 3x + 1 = 0

which represents a quadratic equation.