Phân tích `x(y + z)^2 + y(x + z)^2 + z(x + y)^2 – 4xyz` 10/08/2021 Bởi Alexandra Phân tích `x(y + z)^2 + y(x + z)^2 + z(x + y)^2 – 4xyz`
Đáp án: Giải thích các bước giải: `x(y + z)^2 + y(x + z)^2 + z(x + y)^2 – 4xyz` `= x(y^2 + 2yz + z^2) + y(x^2 + 2xz + z^2) + z(x + y)^2 – 4xyz` `= xy^2 + 2xyz + xz^2 + x^2y + 2xyz + yz^2 + z(x + y)^2 – 4xyz` `=(xy^2 + x^2y) + (xz^2 + yz^2) + z(x + y)^2` `=xy(y + x) + z^2(x + y) + z(x + y)^2` `=(x + y) [xy + z^2 + z(x + y)]` `=(x + y) (xy + z^2 + zx + zy)` `=(x + y) [(x(y +z) + z(y + z)]` `=(x + y) (y + z) (x + z)` Bình luận
$x$$(y+z)^{2}$ + $y$$(x+z)^{2}$ + $z$$(x+y)^{2}$ – $4xyz$ $=$ $xy^{2}$ + $2xyz$ + $xz^{2}$ + $yx^{2}$ + $2xyz$ + $yz^{2}$ + $xz^{2}$ + $2xyz$ + $zy^{2}$ $-4xyz$ $=$ $xy$ $(x+y)$ $+ yz (y+z) + xz(x+z) + xyz + xyz$ $=$ $xy (x+y+z) + yz (x+y+z) + xz (x+z)$ $=$ $(xy+yz) (x+y+z) + xz(x+z)$ $=y (x+y+z) (x+z) + xz (x+z)$ $=(x+z) (xy+ $$y^{2}$ $+yz+xz)$ $=(x+z) [x(x+y)+z(x+y)]$ $=(x+y)(y+z)(x+z)$ Chúc bạn học tốt!^^ Bình luận
Đáp án:
Giải thích các bước giải:
`x(y + z)^2 + y(x + z)^2 + z(x + y)^2 – 4xyz`
`= x(y^2 + 2yz + z^2) + y(x^2 + 2xz + z^2) + z(x + y)^2 – 4xyz`
`= xy^2 + 2xyz + xz^2 + x^2y + 2xyz + yz^2 + z(x + y)^2 – 4xyz`
`=(xy^2 + x^2y) + (xz^2 + yz^2) + z(x + y)^2`
`=xy(y + x) + z^2(x + y) + z(x + y)^2`
`=(x + y) [xy + z^2 + z(x + y)]`
`=(x + y) (xy + z^2 + zx + zy)`
`=(x + y) [(x(y +z) + z(y + z)]`
`=(x + y) (y + z) (x + z)`
$x$$(y+z)^{2}$ + $y$$(x+z)^{2}$ + $z$$(x+y)^{2}$ – $4xyz$
$=$ $xy^{2}$ + $2xyz$ + $xz^{2}$ + $yx^{2}$ + $2xyz$ + $yz^{2}$ + $xz^{2}$ + $2xyz$ + $zy^{2}$ $-4xyz$
$=$ $xy$ $(x+y)$ $+ yz (y+z) + xz(x+z) + xyz + xyz$
$=$ $xy (x+y+z) + yz (x+y+z) + xz (x+z)$
$=$ $(xy+yz) (x+y+z) + xz(x+z)$
$=y (x+y+z) (x+z) + xz (x+z)$
$=(x+z) (xy+ $$y^{2}$ $+yz+xz)$
$=(x+z) [x(x+y)+z(x+y)]$
$=(x+y)(y+z)(x+z)$
Chúc bạn học tốt!^^