Hướng dẫn trả lời:
9)
a) `[5*(x - 2y)^3 + (x - 2y)^2 + 2y - x] ÷ (x - 2y)`
`= [5*(x - 2y)^3 + (x - 2y)^2 - x + 2y] ÷ (x - 2y)`
`= [5*(x - 2y)^3 + (x - 2y)^2 - (x - 2y)] ÷ (x - 2y)`
`= (x - 2y)*[5*(x - 2y)^2 + (x - 2y) - 1] ÷ (x - 2y)`
`= (x - 2y)*{5*[x^2 - 2*x*2y + (2y)^2] + (x - 2y) - 1} ÷ (x - 2y)`
`= (x - 2y)*[5*(x^2 - 4xy + 4y^2) + (x - 2y) - 1] ÷ (x - 2y)`
`= (x - 2y)*(5x^2 - 20xy + 16y^2 + x - 2y - 1) ÷ (x - 2y)`
`= 5x^2 - 20xy + 16y^2 + x - 2y - 1`
b) `[6*(x + y)^3 - 5*(x + y)^2 + 2*(x + y)] ÷ (x + y)`
`= (x + y)*[6*(x + y)^2 - 5*(x + y) + 2] ÷ (x + y)`
`= (x + y)*[6*(x^2 + 2xy + y^2) - 5x - 5y + 2] ÷ (x + y)`
`= (x + y)*(6x^2 + 12xy + 6y^2 - 5x - 5y + 2) ÷ (x + y)`
`= 6x^2 + 12xy + 6y^2 - 5x - 5y + 2`
c) `(x^3 - 8y^3) ÷ (x - 2y)`
`= [x^3 - (2y)^3] ÷ (x - 2y)`
`= (x - 2y)*[x^2 + x*2y + (2y)^2] ÷ (x - 2y)`
`= (x - 2y)*(x^2 + 2xy + 4y^2) ÷ (x - 2y)`
`= x^2 + 2xy + 4y^2`
