What is the HCF of x⁴ − 13x²y² − 300y⁴, x³ − 4x²y − 4xy² − 5y³ and x³ − 125y³ ?

x³ − 125y³ = (x − 5y)(x² + 5xy + 25y²). For the first polynomial, x⁴ − 13x²y² − 300y⁴: let u = x². u² − 13uy² − 300y⁴ = (u − 25y²)(u + 12y²) = (x² − 25y²)(x² + 12y²) = (x − 5y)(x + 5y)(x² + 12y²). The second: x³ − 4x²y − 4xy² − 5y³. Testing x = 5y: 125y³ − 100y³ − 20y³ − 5y³ = 0. So (x − 5y) is a factor. The common factor across all three is (x − 5y).