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

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Алгебра

Авдокея

29 августа, 06:49

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

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Захарьич · Answer 1

(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