Упростите (y²+yx+x²) (y²-yx+x²) (y⁴-y²x²+x⁴) (y⁸-y⁴x⁴+x⁸)

Воспользуемся формулами сокращенного умножения:

a^2 - b^2 = (a + b) (a - b); a^3 + b^3 = (a + b) (a^2 - ab + b^2); a^3 - b^3 = (a - b) (a^2 + ab + b^2); f (x, y) = (y^2 + yx + x^2) (y^2 - yx + x^2) (y^4 - y^2x^2 + x^4) (y^8 - y^4x^4 + x^8); f (x, y) = (y^3 - x^3) / (y - x) * (y^3 + x^3) / (y + x) * (y^6 + x^6) / (y^2 + x^2) * (y^12 + x^12) / (y^4 + x^4); f (x, y) = (y^6 - x^6) / (y^2 - x^2) * (y^6 + x^6) / (y^2 + x^2) * (y^12 + x^12) / (y^4 + x^4); f (x, y) = (y^12 - x^12) / (y^4 - x^4) * (y^12 + x^12) / (y^4 + x^4); f (x, y) = (y^24 - x^24) / (y^8 - x^8); f (x, y) = (y^8 - x^8) (y^16 + y^8x^8 + x^16) / (y^8 - x^8); f (x, y) = y^16 + y^8x^8 + x^16.

Ответ: y^16 + y^8x^8 + x^16.