Ta có  M = x³ + x²y - 2x² - xy - y² +3y + x + 2017

               = x²(x + y - 2) - y(x + y - 2) + x + y - 2 + 2019

thay x + y - 2 = 0 vào M ta có :  M = x².0 - y.0 + 0 + 2019

                                                      = 2019

\(M=x^3+x^2y-2x^2-xy-y^2+3y+x+2017\)

\(=\left(x^3+x^2y-2x^2\right)-\left(xy+y^2-2y\right)+\left(y+x-2\right)+2019\)

\(=x^2\left(x+y-2\right)-y\left(x+y-2\right)+\left(x+y-2\right)+2019\)

\(=\left(x+y-2\right)\left(x^2-y+1\right)+2019\)

Thay \(x+y-2=0\)vào đa thức ta được:

\(M=0.\left(x^2-y+1\right)+2019=2019\)

Bài làm

Ta có: P = x³ + x²y - 2x² - xy - y² + 3y + x + 2017

          P = x³ + x²y - 2x² - xy - y² + 2y + y + x + 2017

          P = ( x³ + x²y − 2x² ) − ( xy + y² − 2y ) + ( x + y − 2 ) + 2019

          P = x²( x + y − 2 ) − y( x + y − 2 ) + ( x + y − 2 ) + 2019

Mà x + y = 2 => x + y - 2 = 0

Thay x + y - 2 = 0 và đa thức P, ta được:

P = x² . 0 - y . 0 + 0 + 2019

P = 0 - 0 + 0 + 2019

P = 2019

Vậy P = 2019 tại x + y = 2

# Học tốt #

\(P=x^3+x^2y-2x^2-xy-y^2+3y+x+2017\)

\(P=\left(x^3+x^2y-2x^2\right)+\left(-xy-y^2+2y\right)+\left(x+y-2\right)+2019\)

\(P=x^2\left(x+y-2\right)-y\left(x+y-2\right)+\left(x+y-2\right)+2019\)

\(P=\left(x^2-y+1\right)\left(x+y-2\right)+2019\)

\(P=0+2019=2019\)

Ta có

\(P=x^3+x^2y-2x^2-xy-y^2+3y+x+2017\)

\(\Leftrightarrow x^3+x^2y-2x^2-xy-y^2+2y+y+x+2017\)

\(\Leftrightarrow\left(x^3+x^2y-2x^2\right)-\left(xy+y^2-2y\right)+\left(x+y-2\right)+2019\)

\(\Leftrightarrow x^2\cdot\left(x+y-2\right)-y\cdot\left(x+y-2\right)+\left(x+y-2\right)+2019\)

Ta có \(x+y=2\Rightarrow x+y-2=0\)

\(\Rightarrow P=2019\)

\(\Rightarrow x^3+x^2y-2x^2-xy-y^2+2y+y+x+2020\)

\(x^2.\left(x+y-2\right)-y\left(x+y-2\right)+y+x+2020\)(1)

Thay x+y-2=0 vào (1) , ta được :

\(x^2.0-y.0+y+x+2020\\ =0+y+x+2020\)

\(=x+y+2022-2\\ =\left(x+y-2\right)+2022\\ \)(2)

Thay x+y-2 vào (2), ta được

\(=0+2022=2022\)

_ Tham khảo thôi ậ, nếu sai thì mong mn thông cảm_

_# yum #_

\(M=x^3+x^2y-2x^2-xy-y^2+3y+x+2017\)

\(\Rightarrow M=\left(x^3+x^2y-2x^2\right)-xy-y^2+2y+y+x-2+2019\)

\(\Rightarrow M=\left(x^3+x^2y-2x^2\right)-\left(xy+y^2-2y\right)+\left(y+x-2\right)+2019\)

\(\Rightarrow M=x^2\left(x+y-2\right)-y\left(x+y-2\right)+\left(x+y-2\right)+2019\)

\(\Rightarrow M=\left(x^2-y+1\right)\left(x+y-2\right)+2019\)

\(\Rightarrow M=\left(x^2-y+1\right).0+2019\)

\(\Rightarrow M=0+2019\)

\(\Rightarrow M=2019\)

M = x³ + x²y - 2x² - xy - y² + 3y + x + 2017

M = (x³ + x²y - 2x²) - (xy + y² - 2y) + (x + y - 2) + 2019

M = x². (x + y - 2) - y(x + y - 2) + (x + y - 2) + 2019 = 2019

\(M = x^3 + x^2y - 2x^2 - xy - y^2 + 3y + x + 2017.\)

\(M=(x^3+x^2y-2x^2)-(xy-y^2+2y)+(x+y-2)+2019\)

\(M=x^2.(x+y-2)-y.(x-y+2)+(x+y-2)+2019\)

\(M=x^2.0-y.0+0+2019\)

\(M=0-0+0+2019\)

\(M=2019\)

$M={}^{}+{}^{}y-2{}^{}-xy-{}^{}+3y+x+2017.$

$M=({}^{}+{}^{}y-2{}^{})-(xy-{}^{}+2y)+(x+y-2)+2019$

$M={}^{}.(x+y-2)-y.(x-y+2)+(x+y-2)+2019$

$M={}^{}.0-y.0+0+2019$