Đáp án:
`6, a^4 - 4a^3 - a^2 + 4a`
`= (a^4 - 4a^3) - (a^2 - 4a)`
`= a^3 (a - 4) - a(a - 4)`
`= (a - 4)(a^3 - a)`
`=(a - 4)(a^2 - 1).a`
`= a(a - 4)(a - 1)(a + 1)`
`7, 16x^4 - x^2 + 4xy - 4y^2`
`= 16x^4 - (x^2 - 4xy + 4y^2)`
`= 16x^4 - [x^2 - 2.x.2y + (2y)^2]`
`= (4x^2)^2 - (x - 2y)^2`
`= (4x^2 + x - 2y)(4x^2 - x + 2y)`
`8, x^2 - y^2 + 2x + 1`
`= (x^2 + 2x + 1) - y^2`
`= (x + 1)^2 - y^2`
`= (x + 1 + y)(x + 1 - y)`
`9, x^3 - 5x^2 - x + 5`
`= (x^3 - 5x^2) - (x - 5)`
`= x^2 (x - 5) - (x - 5)`
`= (x - 5)(x^2 - 1)`
`= (x - 5)(x + 1)(x - 1)`
`10, (x + 1)(x + 2)(x + 3)(x + 4) - 3`
`= [(x + 1)(x + 4)][(x + 2)(x + 3)] - 3`
`= (x^2 + 4x + x + 4)(x^2 + 3x + 2x + 6) - 3`
`= (x^2 + 5x + 4)(x^2 + 5x + 6) - 3`
Đặt `x^2 + 5x = a,` ta được:
`(a + 4)(a + 6) + 2`
`= a^2 + 6a + 4a + 24 - 3`
`= a^2 + 10a + 21`
`= a^2 + 3a + 7a + 21`
`= a(a + 3) + 7(a + 3)`
`= (a + 3)(a + 7)`
`= (x^2 + 5x + 3)(x^2 + 5x + 7)`
