х²(y-z) +y²(z-x) +z²(x-y) Разложить на множители...

Ann0310 @Ann0310

July 2022 1 4 Report

х²(y-z) +y²(z-x) +z²(x-y)
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dtnth

Verified answer

$x^2(y-z)+y^2(z-x)+z^2(x-y)=$
$x^2y-x^2z+y^2z-y^2x+z^2x-z^2y=$
$(x^2y-x^2z)+(y^2z-z^2y)+(z^2x-y^2x)=$
$x^2(y-z)+yz(y-z)-x(y^2-z^2)=$
$x^2(y-z)+yz(y-z)-x(y-z)(y+z)=$
$x^2(y-z)+yz(y-z)-(xy+xz)(y-z)=$
$(x^2+yz-xy-xz)(y-z)=$
$((x^2-xy)-(xz-yz))(y-z)=$
$(x(x-y)-z(x-y))(y-z)=$
$(x-y)(x-z)(y-z)$

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