phân tích đa thức sau thành nhân tử : a,2(x-1)^3-5(x-1)^2 -(x-1) b, x(y-x)^3-y(x-y)^2+y^2(x-y) 28/07/2021 Bởi Reagan phân tích đa thức sau thành nhân tử : a,2(x-1)^3-5(x-1)^2 -(x-1) b, x(y-x)^3-y(x-y)^2+y^2(x-y)
a) $2(x-1)^3-5(x-1)^2-(x-1)$ $=(x-1)[2(x-1)^2-5(x-1)-1]$ $=(x-1)(2x^2-4x+2-5x+4)$ $=(x-1)(2x^2-9x+6)$ b) $x(y-x)^3-y(x-y)^2+y^2(x-y)$ $=-x(x-y)^3-y(x-y)^2+y^2(x-y)$ $=(x-y)[-x(x-y)^2-y(x-y)+y^2]$ $=(x-y)[-x(x^2-2xy+y^2)-xy+y^2+y^2]$ $=(x-y)(-x^3+2x^2y-xy^2-xy+2y^2)$ Bình luận
a) $2(x-1)^3-5(x-1)^2-(x-1)$
$=(x-1)[2(x-1)^2-5(x-1)-1]$
$=(x-1)(2x^2-4x+2-5x+4)$
$=(x-1)(2x^2-9x+6)$
b) $x(y-x)^3-y(x-y)^2+y^2(x-y)$
$=-x(x-y)^3-y(x-y)^2+y^2(x-y)$
$=(x-y)[-x(x-y)^2-y(x-y)+y^2]$
$=(x-y)[-x(x^2-2xy+y^2)-xy+y^2+y^2]$
$=(x-y)(-x^3+2x^2y-xy^2-xy+2y^2)$