What is the HCF of x^3 + y^2 + 3xy - 1 and (x + y)^4 - 1?

Explanation

Assuming a typo in the paper (y^2 should be y^3), the first expression is x^3 + y^3 + 3xy - 1 = (x+y)^3 - 1^3 = (x+y-1)((x+y)^2 + x+y + 1). The second expression is (x+y)^4 - 1 = ((x+y)^2 - 1)((x+y)^2 + 1) = (x+y-1)(x+y+1)((x+y)^2 + 1). Their HCF is (x+y-1).

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