Đáp án:
`a, x^4 - 5x^3 + 15x^2 - 27x`
`= x(x^3 - 5x^2 + 15x - 27`
`= x(x^3 - 9x^2 + 27x - 27 + 4x^2 - 12x)`
`= x[(x^3 - 3.x^2 .3 + 3.x.3^2 - 3^3] + (4x^2 - 12x)]`
`= x[(x - 3)^3 + 4x(x - 3)]`
`= x(x - 3)[(x - 3)^2 + 4x]`
`= x(x - 3)(x^2 - 6x + 9 + 4x)`
`= x(x - 3)(x^2 - 2x + 9)`
`b, x^2 - 4x^2 y^2 + y^2 + 2xy`
`= (x^2 + 2xy + y^2) - 4x^2 y^2`
`= (x + y)^2 - (2xy)^2`
`= (x + y + 2xy)(x + y - 2xy)`
`c, a^2 - b^2 + 4bc - 4c^2`
`= a^2 - (b^2 - 4bc + 4c^2)`
`= a^2 - [b^2 - 2.b.2c + (2c)^2]`
`= a^2 - (b - 2c)^2`
`= [a - (b - 2c)][a + (b - 2c)]`
`= (a - b + 2c)(a + b - 2c)`
`d, 4b^2 c^2 - (b^2 + c^2 - a^2)`
`→` Đề sai
Sửa: `4b^2 c^2 - (b^2 + c^2 - a^2)^2`
`= (2bc)^2 - (b^2 + c^2 - a^2)^2`
`= [2bc + (b^2 + c^2 - a^2)][2bc - (b^2 + c^2 - a^2)]`
`= (2bc + b^2 + c^2 - a^2)(2bc - b^2 - c^2 + a^2)`
`= [(b^2 + 2bc + c^2) - a^2][a^2 - (b^2 - 2bc + c^2)]`
`= [(b + c)^2 - a^2][a^2 - (b - c)^2]`
`= [(b + c) - a][(b + c) + a][a - (b - c)][a + (b - c)]`
`= (b + c + a)(b + c - a)(a - b + c)(a + b - c)`
