Đáp án+Giải thích các bước giải:

`a) ax^3 - 3ax^2 + 3ax - a`

`= a(x^3 - 3x^2 + 3x - 1)`

`= a(x - 1)^3`

`b) x^2 - a^2 + 2ab - b^2`

`= x^2 - (a^2 - 2ab + b^2)`

`= x^2 - (a - b)^2`

`= (x - a + b)(x + a - b)`

`c) (xy + 4)^2 - 4(x + y)^2`

`= (xy + 4)^2 - [ 2(x + y)]^2`

`= (xy + 4 - 2x - 2y)(xy + 4 + 2x + 2y)`

`d) (x + y)^2 + 2x(x + y) + x^2 - (x - z)^2 + 2y(x - z) - y^2`

`= [ (x + y)^2 + 2x(x + y) + x^2] - [ (x - z)^2 - 2y(x - z) + y^2]`

`= (x + y + x)^2 - (x - z + y)^2`

`= (2x + y)^2 - (x - z + y)^2`

`= (2x + y - x + z - y)(2x + y + x - z + y)`

`= (x + z)(3x + 2y - z)`

`e) x^6 - x^4 - 9x^3 + 9x^2`

`= x^4(x^2 - 1) - 9x^2(x - 1)`

`= x^4(x - 1)(x + 1) - 9x^2 ( x - 1)`

`= (x - 1) [ x^4 (x + 1) - 9x^2]`

`= (x - 1) [ x^2 . (x^3 + x^2) - 9 .x^2]`

`= x^2(x - 1)(x^3 + x^2 - 9)`