Phân tích đa thức thành nhân tử

Đáp án+Giải thích các bước giải:

 Bài 2:

     1) x² - y² - 2x + 2y

<=> (x² - y²) - (2x -2y)

<=> (x+y) (x-y) - 2 (x-y)

<=> (x-y) (x+y-2)

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     2) 2x + 2y - x² - xy

<=> (2x -x²) + (2y - xy)

<=> x (2 -x) + y (2-x)

<=> (2-x) (x+y)

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     3) 3a² -6ab + 3b² - 12c²

<=> 3 ( a² - 2ab + b² - 4c²)

<=> 3 [ ( a² - 2ab + b²) - 4c²]

<=> 3 [ (a-b)² - (2c)²]

<=> 3 (a-b -2c) (a-b +2c)

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     4) x² - 25 + y² + 2xy

<=> (x² + 2xy + y²) - 25

<=> (x+y)² - 5²

<=> ( x+y -5) ( x+y +5)

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     5) a² + 2ab + b² -ac - bc

<=> ( a² + 2ab + b²) - (ac +bc)

<=> (a+b)² - c(a+b)

<=> (a+b) (a+b-c)

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     6) x² - 2x -4y² - 4y

<=> (x² - 4y²) - (2x + 4y)

<=> (x-2y) (x+2y) - 2 (x+2y)

<=> (x+2y) (x-2y -2)

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      7) x²y - x³ - 9y + 9x

<=>  (x²y -x³) - (9y - 9x)

<=> x² (y -x) - 9 (y-x)

<=> (y-x) (x² -9)

<=> (y-x) (x-3) (x+3)

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      8) x² (x-1) + 16 (1-x)

<=> x² ( x-1) - 16 (x-1)

<=> (x-1) (x² -16)

<=> (x-1) (x-4) (x+4)

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      9) 3x² - 6x + 9x²

<=>12x² - 6x

<=> 6x (2x -1)

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  10) 10x (x-y) - 6y (y-x)

<=> 10x (x-y) + 6y (x-y)

<=> (x-y) (10x + 6y)

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   11) 3x² + 5y - 3xy - 5x

<=> (3x² - 3xy) - (5x - 5y)

<=> 3x (x-y) - 5 (x-y)

<=> (x-y) (3x-5)

----------------------------------------------------

   12) $x^{5}$ - 3$x^{4}$ + $3x^{3}$ - $x^{2}$ 

<=> x² ( x³ - 3x² + 3x - 1)

<=> x² (x-1)³

<=> x² ( x-1) ( x² + x +1)

----------------------------------------------------

   13) (x² +1)² - 4x²

<=> (x² +1)² - (2x)²

<=> ( x² + 1 - 2x) ( x² + 1 + 2x)

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    14) x² -4x -5

<=> x² - 4x + 4 - 9

<=> (x² -4x + 4) - 9

<=> (x-2)² - 3²

<=> (x-2-3) (x-2 +3)

<=> (x-5) (x +1)

----------------------------------------------------------

   15) x² + 8x + 15

<=> x² + 8x + 16 -1

<=> (x² + 8x + 16) -1

<=> (x +4)² - 1²

<=> (x+4 -1) (x+4 +1)

<=> ( x+3) ( x+5)

------------------------------------------------------------

    16) $81x^{4}$ -4

<=> (3x)² × (3x)² - 4

<=> (3x)² × [ (3x) ² -2²]

<=> (3x)² (3x -2) (3x+2)

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     17) 2x² + 3x -5

<=> 2x² - 2x + 5x -5

<=> (2x² -2x) + (5x -5)

<=> 2x (x-1) + 5 (x-1)

<=> (x-1) (2x+5)

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     18) 16x - 5x² - 3

<=> 15x + x - 5x² - 3

<=> ( 15x - 5x²) - ( 3-x)

<=> 5x ( 3 -x) - (3-x)

<=> (3-x) (5x-1)

#sotuyet