Phân tích đa thức thành nhân tử xy(x-y)-xz(x+z)+yz(2x+z-y)

Question

Phân tích đa thức thành nhân tử
xy(x-y)-xz(x+z)+yz(2x+z-y)

in progress 0
King 4 years 2020-11-01T20:44:58+00:00 2 Answers 72 views 0

Answers ( )

  1. quangkhai
    0
    2020-11-01T20:46:26+00:00
    Reply

    `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)`

  2. Adela
    0
    2020-11-01T20:46:32+00:00
    Reply

    Đáp án:

    $(x-y)(x+z)(y-z)$

    Giải thích các bước giải:

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

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

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

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

    $=xy(x-y)-z(x-y)^2-z^2(x-y)$

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

    $=(x-y)[y(x+z)-z(x+z)]$

    $=(x-y)(x+z)(y-z)$

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )