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wolf2k
@wolf2k
July 2022
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xy^2+x^2y-x^3-y^3 разложите на множители
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ShirokovP
Verified answer
xy^2 + x^2y - (x^3 + y^3) =
= xy (x + y) - (x + y) (x^2 - xy + y^2
) =
= (x + y)(xy - x^2 + xy - y^2) =
=
(x + y)( - x^2 + 2xy - y^2) =
= - (x + y)(x^2 - 2xy + y^2) =
= - (x + y)(x - y)^2
2 votes
Thanks 1
ShirokovP
обнови там была ошибка
ShirokovP
я исправил
wolf2k
спасибо!
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Answers & Comments
Verified answer
xy^2 + x^2y - (x^3 + y^3) == xy (x + y) - (x + y) (x^2 - xy + y^2) =
= (x + y)(xy - x^2 + xy - y^2) =
= (x + y)( - x^2 + 2xy - y^2) =
= - (x + y)(x^2 - 2xy + y^2) =
= - (x + y)(x - y)^2