(y²+yx+x²)(y²-yx+x²)(y⁴-y²x²+x⁴)(y⁸-y⁴x⁴+x⁸) - вопрос №30822 от lilcutthroat 06.06.2021 11:56

Question

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

lilcutthroat · Answer

(y²+yx+x²)(y²-yx+x²)(y⁴-y²x²+x⁴)(y⁸-y⁴x⁴+x⁸)=y^16+x^8y^8+y^16

(y²+yx+x²)(y²-yx+x²)=(y^2+x^2)^2-x^2y2=y^4+x^2y^2+y^4,

(y^4+x^2y^2+y^4)(y^4-x^2y^2+y^4)=(x^4+y^4)^2-(x^2y^2)^2=

=y^8+x^4y^4+y^8,

(y^8+x^4y^4+y^8)(y^8-x^4y^4+y^8)=(x^8+y^8)^2-(x^4y^4)^2=

=y^16+x^8y^8+y^16,

ответ: y^16+x^8y^8+y^16