Đáp án:
`a, 4x^4 - 32x^2 + 1`
`= 4x^4 + 4x^2 + 1 - 32x^2 - 4x^2`
`= [(2x^2)^2 + 2.2x^2 .1 + 1^2] - 36x^2`
`= (2x^2 + 1)^2 - (6x)^2`
`= (2x^2 + 6x + 1)(2x^2 - 6x + 1)`
`b, x^2 - 2x - 4y^2 - 4y`
`= x^2 - 2x + 1 - 4y^2 - 4y - 1`
`= (x^2 - 2x + 1) - (4y^2 + 4y + 1)`
`= (x^2 - 2.x.1 + 1^2) - [(2y)^2 + 2.2y.1 + 1^2]`
`= (x - 1)^2 - (2y + 1)^2`
`= [(x - 1) - (2y + 1)][(x-1) + (2y +1)]`
`= (x - 1 - 2y - 1)(x - 1 + 2y + 1)`
`= (x - 2y - 2)(x + 2y)`
`c, x^4 - 2x^3 + 2x - 1`
`= x^4 - 2x^3 + x^2 - x^2 + 2x - 1`
`= (x^4 - 2x^3 + x^2) - (x^2 - 2x + 1)`
`= x^2 (x^2 - 2x + 1) - (x^2 - 2x + 1)`
`= (x^2 - 2x + 1)(x^2 - 1)`
`= (x - 1)^2 (x - 1)(x + 1)`
`= (x - 1)^3 (x + 1)`
`d, x^4 + 2x^3 - 4x - 4`
`= x^4 + 2x^3 + x^2 - x^2 - 4x - 4`
`= (x^4 + 2x^3 + x^2) - (x^2 + 4x + 4)`
`= x^2 (x^2 + 2x + 1) - (x^2 + 2.x.2 + 2^2)`
`= x^2 (x + 1)^2 - (x + 2)^2`
`= [x(x + 1)]^2 - (x + 2)^2`
`= [x(x + 1) - (x + 2)][x(x + 1) + (x + 2)]`
`= (x^2 + x - x - 2)(x^2 + x + x + 2)`
`= (x^2 - 2)(x^2 + 2x + 2)`
`C2: x^4 + 2x^3 - 4x - 4`
`= x^4 + 2x^3 + 2x^2 - 2x^2 - 4x - 4`
`= (x^4 + 2x^3 + 2x^2) - (2x^2 + 4x + 4)`
`= x^2 (x^2 + 2x + 2) - 2(x^2 + 2x + 2)`
`= (x^2 + 2x + 2)(x^2 - 2)`
