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Đáp án:
`a) (x + 4)(x - 2)`
`b) (x + 2)(x + 3)`
`c) 4(x - 2)(x - 1)`
`d) (3x+5y)(x+y)`
`e) (x + 4)(x + 2)`
`f) 2(x + 1)(x + 6)`
`g) (3x + 5)(3x + 3)`
`h) (x + y)(6x - 7y)`
Giải thích các bước giải:
`a) x^2 + 2x - 8`
` = x^2 + 2x + 1 - 9`
` = (x + 1)^2 - 3^2`
` = (x + 1 + 3)(x + 1 - 3)`
` = (x + 4)(x - 2)`
________________________
`b) x^2 + 5x + 6`
` = x^2 + 2.x . 5/2 + 25/4 - 1/4`
` = (x + 5/2)^2 - 1/4`
` = (x + 5/2 - 1/2)(x + 5/2 + 1/2)`
` = (x + 2)(x + 3)`
__________________________
`c) 4x^2 - 12x + 8`
` = (2x)^2 - 2.2x.3 + 9 - 1`
` = (2x - 3)^2 - 1`
` = (2x - 3 - 1)(2x - 3 + 1)`
` = (2x - 4)(2x - 2)`
` = 4(x - 2)(x - 1)`
_________________________
`d) 3x^2 + 8xy + 5y^2`
`= 3x^2 + 3xy + 5xy + 5y^2`
`= 3x( x+y) + 5y( x+y)`
`= (3x+5y)(x+y)`
__________________________
`e) x^2 + 6x + 8`
` = x^2 + 6x + 9 - 1`
` = (x + 3)^2 - 1`
` = (x + 3 + 1)(x + 3 - 1)`
` = (x + 4)(x + 2)`
__________________________
`f) 2x^2 + 14x + 12`
` = 2(x^2 + 7x + 6)`
` = 2(x^2 + x + 6x + 6)`
` = 2[x(x + 1) + 6(x + 1)]`
` = 2(x + 1)(x + 6)`
__________________________
`g) 9x^2 + 24x + 15`
` = (3x)^2 + 2.3x.4 + 16 - 1`
` = (3x + 4)^2 - 1`
` = (3x + 4 + 1)(3x + 4 - 1)`
` = (3x + 5)(3x + 3)`
__________________________
`h) 6x^2 - xy - 7y^2`
` = (x + y)(6x - 7y)`
