phân tích thành nt 1)2xy-x^2-y^2+9 2)X^2_x+(2x+1)(x-1) 3)(x+2)^2+2.x+2.(x-1)+(x-1)^2 4)2x^2+4x+2-8y^2 5)X^2+2x-y^2+1 6)X^2+2xy+2y^2+xy

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1. 1)

   $2xy – x² – y² + 9$

   $= -(x² – 2xy + y²) + 9$

   $= 3² – (x – y)²$

   $= (3 + x – y)(3 – x + y)$

   2)

   $x² – x + (2x + 1)(x – 1)$

   $= x(x – 1) + (2x + 1)(x – 1)$

   $= (x – 1)(x + 2x + 1)$

   $= (x – 1)(3x + 1)$

   3)

   $(x + 2)² + 2(x + 2)(x – 1) + (x – 1)²$

   $=(x + 2 + x – 1)²$

   $= (2x + 1)²$

   4) $2x² + 4x + 2 – 8y²$

   $= 2(x² + 2x + 1 – 4y²)$

   $= 2((x + 1)² – (2y)²)$

   $= 2(x + 1 – 2y)(x + 1 + 2y)$

   5)

   $x² + 2x – y² + 1$

   $= x² + 2x + 1 – y²$

   $= (x + 1)² – y²$

   $= (x + 1 – y)(x + 1 + y)$

   6)

   $x² + 2xy + 2y² + xy$

   $= x² + xy + 2y² + 2xy$

   $= x(x + y) + 2y(x + y)$

   $= (x + 2y)(x + y)$

    

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2. Đáp án+Giải thích các bước giải:

    `1) 2xy-x^2-y^2+9`

   `=-[(x^2-2xy+y^2)-9]`

   `=-[(x-y)^2-3^2]`

   `=-(x-y-3)(x-y+3)`

    `2) x^2-x+(2x+1)(x-1)`

   `=x(x-1)+(2x+1)(x-1)`

   `=(x-1)(x+2x+1)`

    `3) (x+2)^2+2.(x+2).(x-1)+(x-1)^2`

   `= (x+2+x-1)^2`

   `= (2x+1)^2`

    `4) 2x^2+4x+2-8y^2`

   `=-2.(4y^2-x^2-2x-1)`

   `= -2.[(2y)^2-(x^2+2x+1)]`

   `= -2. [(2y)^2-(x+1)^2]`

   `= -2.(2y-x-1)(2y+x+1)`

    `5) x^2+2x-y^2+1`

   `=(x^2+2x+1)-y^2`

   `= (x+1)^2-y^2`

   `= (x+1-y)(x+1+y)`

    `6) x^2+2xy+2y^2+xy`

   `= x(x+2y)+y(x+2y)`

   `=(x+y)(x+2y)`

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