Đáp án:
 `a, 4x^4 - 32x^2 + 1`
`= (4x^4 + 4x^2 + 1) - 36x^2`
`= [(2x^2)^2 + 2.2x^2 .1 + 1^2] - 36x^2`
`= (2x^2 + 1)^2 - (6x)^2`
`= (2x^2 + 1 + 6x)(2x^2 + 1 - 6x)`
`b, x^6 + 27`
`= (x^2)^3 + 3^3`
`= (x^2 + 3)[(x^2)^2 - x^2 .3 + 3^2]`
`= (x^2 + 3)(x^4 - 3x^2 + 9)`
`= (x^2 + 3)[x^4 + 6x^2 + 9 - 9x^2]`
`= (x^2 + 3){[(x^2)^2 + 2.x^2 .3 + 3^2] - 9x^2}`
`= (x^2 + 3)[(x^2 + 3)^2 - (3x)^2]`
`= (x^2 + 3)(x^2 + 3 - 3x)(x^2 + 3 + 3x)`
`c, 3(x^4 + x^2 + 1) - (x^2 + x + 1)^2`
`= 3(x^4 + 2x^2 + 1 - x^2) - (x^2 + x + 1)^2`
`= 3[(x^2)^2 + 2.x^2 . 1+ 1^2 - x^2] - (x^2 + x + 1)^2`
`= 3[(x^2 + 1)^2 - x^2] - (x^2 + x + 1)^2`
`= 3(x^2 + 1 + x)(x^2 + 1 - x) - (x^2 + x + 1)^2`
`= (x^2 + x + 1)[3(x^2 - x + 1) - (x^2 + x + 1)]`
`= (x^2 + x + 1)(3x^2 - 3x + 3 - x^2 - x - 1)`
`= (x^2 + x + 1)(2x^2 - 4x + 2)`
`= (x^2 + x + 1).2.(x^2 - 2x + 1)`
`= 2(x^2 + x + 1)(x - 1)^2`
`d, (2x^2 - 4)^2 + 9`
`= (2x^2)^2 - 2.2x^2 .4 + 4^2 + 9`
`= 4x^4 - 16x^2 + 16 + 9`
`= 4x^4 - 16x^2 + 25`
`= 4x^4 + 20x^2 + 25 - 36x^2`
`= [(2x^2)^2 + 2.2x^2 .5 + 5^2] - 36x^2`
`= (2x^2 + 5)^2 - (6x)^2`
`= (2x^2 + 5 + 6x)(2x^2 + 5 - 6x)`