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.