The GCD of x <sup>A. 1

B. x + y

C. x – y

D. x2 – y2</sup>

Given two polynomials: x² – 2xy + y² and x⁴ – y⁴

Required: To find GCD of the given two polynomials

Let f(x) = x² – 2xy + y² and g(x) = x⁴ – y⁴

f(x) = x² – 2xy + y²

⇒ f(x) = (x–y)²

g(x) = x⁴ – y⁴

⇒ g(x) = (x²)² – (y²)²

⇒ g(x) = (x² – y²)(x² + y²) (∵ a²–b² = (a–b)(a + b))

⇒ g(x) = (x–y)(x + y)(x² + y²) (∵ a²–b² = (a–b)(a + b))

∴ The GCD of given two polynomials is (x–y)

∴ Correct Option is - Option (C)