Q. 95.0( 1 Vote )

The GCD of x A. 1

B. x + y

C. x – y

D. x2 – y2

Answer :

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)

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