21 БАЛЛ!!Разложить на множители[tex]x ^{2} (y - z) + y^{2}(z - x) + z^{2}(x - y)[/tex]. Created by lev25340. algebra-ru

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lev25340 @lev25340

July 2022 1 2 Report

21 БАЛЛ!!
Разложить на множители

[tex]x ^{2} (y - z) + y^{2}(z - x) + z^{2}(x - y)[/tex]

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igorShap

Verified answer

$x ^{2} (y - z) + y^{2}(z - x) + z^{2}(x - y)=x ^{2} y -x^2 z + y^{2}z - y^2x + z^{2}x - z^2y=(x^2-z^2)y-xz(x-z)-y^2(x-z)=(x-z)((x+z)y-xz-y^2)=(x-z)(xy+zy-xz-y^2)=(x-z)(y(x-y)-z(x-y))=(x-z)(x-y)(y-z)$

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lev25340 August 2022 | 0 Ответы

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