x 3 - x + 3 x 2 y + 3 x y 2 + y 3 - y = x 3 + 3 x 2 y + 3 x y 2 + y 3 - x - y = x + y 3 - x - y = x + y x + y 2 - 1 = x + y x + y + 1 x + y - 1

\(=\left(x+y\right)^3-\left(x+y\right)=\left(x+y\right)\left(x^2+2xy+y^2-1\right)\)

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

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

\(=\left(x+y\right)\left(x+y+1\right)\left(x+y-1\right)\)

= (x³ + 3x²y + 3xy² + y³) - (x+y)

= (x + y)³ - (x + y)

= (x + y).[(x+y)² - 1 ]

= (x + y).(x + y - 1).(x + y + 1)

c) \(3x+3y-x^2-2xy-y^2=3\left(x+y\right)-\left(x+y\right)^2=\left(x+y\right)\left(3-x-y\right)\)d) \(=\left(x+y\right)^3-\left(x+y\right)=\left(x+y\right)\left[\left(x+y\right)^2-1\right]\)

\(=\left(x+y\right)\left(x+y+1\right)\left(x+y-1\right)\)

\(c,=3\left(x+y\right)-\left(x+y\right)^2=\left(3-x-y\right)\left(x+y\right)\\ d,=\left(x+y\right)^3-\left(x+y\right)=\left(x+y\right)\left[\left(x+y\right)^2-1\right]\\ =\left(x+y\right)\left(x+y-1\right)\left(x+y+1\right)\)

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

d) \(\left(x+y\right)^3-\left(x+y\right)=\left(x+y\right)\left[\left(x+y\right)^2-1\right]=\left(x+y\right)\left(x+y-1\right)\left(x+y+1\right)\)

=(x-y)^3-(x-y)(x+y)

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

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

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

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

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

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

Kết quả: 27

Đáp án: 8