bonjour Factorise les expressions suivantes a.(2x-3)(x+2)-5(2x-3) b.(5x+1)(3x-5)-(x-3)(5x+1) c.(3x+2)(-5x-7)-(3x+2)(x+7) d.(5x-8)(7x-3)-(7x-3)² Merci de m'avoir

bonjour

a)    ( 2 x - 3 ) ( x + 2 - 5 ) = ( 2 x - 3 ) ( x - 3 )

b) ( 5 x + 1 ) ( 3 x - 5 - x + 3 ) = ( 5 x + 1 ) ( 2 x - 2 ) = 2 ( 5 x + 1 ) ( x - 1  

c)  ( 3 x + 2 ) ( - 5 x - 7 - x - 7 ) = ( 3 x + 2 ) ( - 6 x - 14 )

d)  ( 7 x - 3 ) ( 5 x - 8 - 7 x + 3 ) = ( 7 x - 3 ) ( - 2 x - 5 )

a)

 (2x-3)(x+2) - 5(2x-3)

= (2x-3)(x+2) - 5(2x-3)

= (2x -3)[(x+2)-5]

= (2x -3)(x -3)

b)

   (5x+1)(3x-5) - (x-3)(5x+1)

 = (5x+1)(3x-5) - (x-3)(5x+1)

 = (5x + 1)[3x - 5) - (x - 3)]

 = (5x + 1)(3x -5 -x + 3)

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

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

c  (3x+2)(-5x-7) - (3x+2)(x+7)

   = (3x+2)(-5x-7) - (3x+2)(x+7)

  = (3x + 2)[(-5x - 7) - (x + 7)]

 =  (3x + 2)(-5x - 7 - x - 7)

= (3x + 2)(-6x - 14)

= -2(3x - 2)(3x + 7)

d (5x-8)(7x-3) - (7x-3)²

  = (5x-8)(7x-3)  - (7x-3)(7x - 3)

   =  (5x-8)(7x-3) - (7x-3)(7x - 3)

  = (7x -3)[(5x - 8) - (7x - 3)]

  = (7x - 3)(5x -8 - 7x +3)

  = (7x -3)(-2x -5)