a: x+y+1=0
=>x+y=-1
\(A=x^3+x^2y-xy^2-y^3+x^2+2x+2y+3-y^2\)
\(=x^2\left(x+y\right)-y^2\left(x+y\right)+x^2-y^2+2\left(x+y\right)+3\)
\(=-x^2+y^2+x^2-y^2-2+3=1\)
=>ĐPCM
b: \(B=x^3+2x^2y+xy^2+x^2+xy+x+y+5\)
\(=x\left(x^2+2xy+y^2\right)+x\left(x+y\right)+\left(x+y\right)+5\)
\(=x\left(x+y\right)^2+x\left(x+y\right)+\left(x+y\right)+5\)
=x-x+(-1)+5=4
=>ĐPCM
c: \(C=x^3+2xy\left(x+y\right)+y^3+x^2+y^2+xy+2\)
\(=\left(x^3+y^3\right)+x^2-2xy+y^2+xy+2\)
\(=\left(x+y\right)^3-3xy\left(x+y\right)+x^2-xy+y^2+2\)
\(=-1+3xy+x^2-xy+y^2+2=-1+\left(x+y\right)^2+2\)
=1+1
=2
Đúng 3
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