The HCF of (x 4 - y 4) and (x 6 - y 6) is

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

Let f (x) = (x4 - y4) = (x2 - y2) (x2 + y2) = (x - y) (x + y) (x2 + y2) and g(x) = (x6 - y6) = (x3)2 - (y3)2 = (x3 + y3) (x3 - y3) = (x + y) (x2 - xy + y2) (x - y)(x2 + xy + y2) = (x - y) (x + y) (x2 - xy + y2) (x2 + xy + y2) ∴ HCF of [f(x), g(x)] = (x - y) (x + y) = x2 - y2

The HCF of (x 4 - y 4) and (x 6 - y 6) is

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