Toán Phân tích đa thức thành nhân tử xy(x-y)-xz(x+z)+yz(2x+z-y) 11/07/2021 By Arya Phân tích đa thức thành nhân tử xy(x-y)-xz(x+z)+yz(2x+z-y)
`xy(x-y)-xz(x+z)+yz(2x+z-y)` `= xy(x-y)-xz(x+z)+yz(x+z+x-y)` `=xy(x-y)-xz(x+z)+yz(x+z)+yz(x-y)` `=(x-y)(xy+yz)+(z+x)(yz-xz)` `=y(x-y)(x+z)-z(x+z)(x-y)` `=(y-z)(x-y)(z+x)` Trả lời
Đáp án: $(x-y)(x+z)(y-z)$ Giải thích các bước giải: $xy(x-y)-xz(x+z)+yz(2x+z-y)$ $=x^2y-xy^2-x^2z-xz^2+2xyz+yz^2-y^2z$ $=(x^2y-xy^2)-(x^2z-2xyz+y^2z)-(xz^2-yz^2)$ $=xy(x-y)-z(x^2-2xy+y^2)-z^2(x-y)$ $=xy(x-y)-z(x-y)^2-z^2(x-y)$ $=(x-y)(xy-xz+yz-z^2)$ $=(x-y)[y(x+z)-z(x+z)]$ $=(x-y)(x+z)(y-z)$ Trả lời
`xy(x-y)-xz(x+z)+yz(2x+z-y)`
`= xy(x-y)-xz(x+z)+yz(x+z+x-y)`
`=xy(x-y)-xz(x+z)+yz(x+z)+yz(x-y)`
`=(x-y)(xy+yz)+(z+x)(yz-xz)`
`=y(x-y)(x+z)-z(x+z)(x-y)`
`=(y-z)(x-y)(z+x)`
Đáp án:
$(x-y)(x+z)(y-z)$
Giải thích các bước giải:
$xy(x-y)-xz(x+z)+yz(2x+z-y)$
$=x^2y-xy^2-x^2z-xz^2+2xyz+yz^2-y^2z$
$=(x^2y-xy^2)-(x^2z-2xyz+y^2z)-(xz^2-yz^2)$
$=xy(x-y)-z(x^2-2xy+y^2)-z^2(x-y)$
$=xy(x-y)-z(x-y)^2-z^2(x-y)$
$=(x-y)(xy-xz+yz-z^2)$
$=(x-y)[y(x+z)-z(x+z)]$
$=(x-y)(x+z)(y-z)$