bai 1 a,15x^2y+20xy^2-25xy b,x^2-y^2+2x-2y c,x^2y-x^3-9y+9x d,x^2+8x+15

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1. Đáp án:

   a, Ta có : 

   `15x^2y + 20xy^2 – 25xy`

   ` = 5xy.3x + 5xy.4y – 5xy.5`

   ` = 5xy(3x + 4y – 5)`

   b, Ta có : 

   `x^2 – y^2 + 2x – 2y`

   ` = (x – y)(x + y) + 2(x – y)`

   ` = (x – y)(x + y + 2)`

   c, Ta có : 

   `x^2y – x^3 –  9y + 9x`

   ` = (x^2y – x^3) – (9y – 9x)`

   ` = x^2(y – x) – 9(y – x)`

   ` = (y – x)(x^2 – 9)`

   ` = (y – x)(x – 3)(x + 3)`

   d, Ta có : 

   `x^2 + 8x + 15`

   ` = x^2 + 8x + 16 – 1`

   ` = x^2 + 2.x.4 + 4^2 – 1^2`

   ` = (x + 4)^2 – 1^2`

   ` = (x + 4 – 1)(x + 4 + 1)`

   ` = (x + 3)(x + 5)`

   Giải thích các bước giải:

    

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2. a,

   15x^2y+20xy^2−25xy

   =5xy.3x+5xy.4y−5xy.5

   =5xy(3x+4y−5)

   b,

   x^2−y^2+2x−2y

   =(x−y)(x+y)+2(x−y)

   =(x−y)(x+y+2)

   c,

   x2^y−x^3− 9y+9x

   =(x^2y−x^3)−(9y−9x)

   =x^2(y−x)−9(y−x)

   =(y−x)(x^2−9)

   =(y−x)(x−3)(x+3)

   d,

   x^2+8x+15

   =x^2+2.x.4+4^2−1

   =(x+4)^2−1^2

   =(x+4−1)(x+4+1)

   =(x+3)(x+5)

    

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