Đáp án:
`a, [(3x - 2)(x + 1) - (2x + 5)(x^2 - 1)] : (x + 1)`
`= [(3x - 2)(x + 1) - (2x + 5)(x + 1)(x - 1)] : (x + 1)`
`= (x + 1)[3x - 2 - (2x + 5)(x - 1)] : (x + 1)`
`= 3x - 2 - (2x + 5)(x - 1)`
`= 3x - 2 - 2x^2 + 2x - 5x + 5`
`= (3x + 2x - 5x) - 2x^2 + (-2 + 5)`
`= -2x^2 + 3`
`b, (2x - 1)^2 - 2(2x - 1)(3 - x) + (3 - x)^2`
`= [(2x - 1) - (3 - x)]^2`
`= (2x - 1 - 3 + x)^2`
`= (3x - 4)^2`
`= (3x)^2 - 2.3x.4 + 4^2`
`= 9x^2 - 24x + 16`
`c, (x - 1)^3 - (x + 1)(x^2 - x + 1) - (3x + 1)(1 - 3x)`
`= x^3 - 3x^2 + 3x - 1 - (x^3 + 1^3) - [1^2 - (3x)^2]`
`= x^3 - 3x^2 + 3x - 1 - x^3 - 1 - 1 + 9x^2`
`= (x^3 - x^3) + (-3x^2 + 9x^2) + 3x + (-1 - 1- 1)`
`= 6x^2 + 3x - 3`