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Bài `1:`
`a, 4x^2 - 8xy + 4y^2`
`= 4(x^2 - 2xy + y^2)`
`= 4(x - y)^2`
`b, x^2 - y^2 - 5x + 5y`
`= (x - y)(x + y) - 5(x - y)`
`= (x - y)(x + y - 5)`
`c, 5x(x - 1) - 3x^2 (1 - x)`
`= 5x(x - 1) + 3x^2 (x - 1)`
`= (x - 1)(5x + 3x^2)`
`= x(x - 1)(5 + 3x)`
`d, 3x^2 - 6xy + 3y^2 - 12z^2`
`= 3(x^2 - 2xy + y^2 - 4z^2)`
`= 3[(x - y)^2 - (2z)^2]`
`= 3(x - y - 2z)(x - y + 2z)`
Bài `2:`
`a, 4x^2 - y^2 + 4x + 1`
`= (4x^2 + 4x + 1) - y^2`
`= (2x + 1)^2 - y^2`
`= (2x -y + 1)(2x + y + 1)`
`b, 36 + 2xy - x^2 - y^2`
`= 36 - (x^2- 2xy + y^2)`
`= 6^2 - (x - y)^2`
`= (6 - x + y)(6 + x - y)`
`c, x^5 - 3x^4 + 3x^3 - x^2`
`= x^2 (x^3 - 3x^2 + 3x - 1)`
`= x^2 (x - 1)^3`
`d, x^3 - x^2 - 5x + 125`
`= x^3 + 5x^2 - 6x^2 - 30x + 25x +125`
`= x^2 (x + 5) - 6x(x + 5) + 25(x + 5)`
`= (x + 5)(x^2 - 6x + 25)`
Bài `3:`
`a, 6x^2 - 5x + 1`
`= 6x^2 - 3x - 2x + 1`
`= 3x(2x - 1) - (2x - 1)`
`= (2x - 1)(3x - 1)`
`b, x^2- 2x - 9y^2 + 6y`
`= (x^2 - 2x + 1) - (9y^2 - 6y + 1)`
`= (x - 1)^2 - (3y - 1)^2`
`= (x - 1 - 3y + 1)(x - 1 + 3y - 1)`
`= (x - 3y)(x + 3y - 2)`
`c, x^2 + 2x - 15`
`= (x^2 + 2x + 1) - 16`
`= (x + 1)^2- 4^2`
`= (x +1 - 4)(x + 1 + 4)`
`= (x - 3)(x + 5)`
`d, (x^2 + 1)^2 - 4x^2`
`= (x^2 + 1)^2 - (2x)^2`
`= (x^2 - 2x + 1)(x^2 + 2x + 1)`
`= (x - 1)^2 (x +1)^2`
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