Question

Which polynomial equation is a valid identity?

Answer 1

D

Explanation:

Expand factors using FOIL

A

(x + 1)² - x² = x² + 2x + 1 - x² = 2x + 1 ≠ 1 ← False

B

(5x - 2)² + 4 = 25x² - 20x + 4 + 4 = 25x² - 20x + 8 ≠ 25x² - 20x ← False

C

(x + 2y)(x - 2y) = x² - 4y² ≠ x² + 4xy - 4y² ← False

D

(2x + y)(- y - 2x) = - 2xy - 4x² - y² - 2xy = - 4x² - y² - 4xy ← True