1. thu gọn a) M=(x+2)^3-(x-1)^3 b) N=(x-3)^3-(x+1)^3 2) cho a+b=8, a

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1. 1 . Thu gọn :

   a) M= ( x + 2 )³ – ( x – 1 )³

           = x³ + 6x² + 12x + 8 – ( x³ – 3x² + 3x – 1 )

           = x³ + 6x² + 12x + 8 – x³ + 3x² – 3x + 1

           = 9x² + 9x + 9

   b) N = ( x – 3 )³ – ( x + 1 )³

            = x³ – 9x² + 27x – 27 – ( x³ + 3x² + 3x + 1 )

           = x³ – 9x² + 27x – 27 – x³ – 3x² – 3x – 1

           = -12x² + 24x – 28

   2 . 

   A = a³ + b³

       = ( a + b )( a² – ab + b² )

       = ( a + b )[( a² + b² ) – ab ]

       = ( a + b )[( a² + b² + 2ab – 2ab ) – ab ]

       = ( a + b )[ ( a + b )² – 3ab ]

   Thay số vào ta có :

      ( a + b )[ ( a + b )² – 3ab ] 

   = 8 . ( 8² – 3 . 15 )

   = 152

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2. `a)`

   ` M = (x+2)^3 – (x-1)^3`

   ` = x^3 + 6x^2 + 12x + 8 – (x^3 – 3x^2 + 3x -1)`

   ` = x^3 + 6x^2 +12x + 8- x^3 +3x^2 – 3x +1`

   `= 9x^2 +9x +9`

   ` = 9(x^2+x+1)`

   `b)`

   ` N = (x-3)^3 – (x+1)^3`

   ` = ( x^3 – 9x^2+ 27x – 27) – (x^3 + 3x^2 +3x +1)`

   ` = x^3 -9x^2 +27x – 27 – x^3 -3x^2 -3x -1`

   ` = -12x^2 + 24x- 28`

   `2)`

   ` A = a^3 +b^3 = (a+b)(a^2 – ab +b^2) = 8(a^2 – ab + b^2)`

   ` = 8 ( a^2 + 2ab + b^2 – 3ab)`

   ` = 8 [ (a+b)^2 – 3ab]`

   ` = 8 . ( 8^2 – 3 .15)`

   ` = 152`

    

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