Développer et réduire les expressions suivantes : a) 2(x+1)(x+2)+ 3(x+7)(x - 2) b) 5(-2x+3)(-2x +1)- 2(x+1)^2 c) 4(x-3)^2 - 3 (x+1)(-2x+4) d) (3x+5)^2 - (2x - 3

a) 2(x+1)(x+2)+3(x+7)(x-2)

    =(2x+1)(x+2)+(3x+21)(x-2)

    =2x²+4x+x+2+3x²-6x+21x-42

    =5x²+20x-40

a) 2(X+1)(X+2)+ 3(X+7)(X - 2)

   = 2 x (X+1) x (X+2)+ 3 x (X+7) x (X - 2)

   = (2 x X) + (2 x 1) x (2 x X) + (2 x 2) + (3 x X) + (3 x 7) x (3 x X) - (3 x 2)

   = 2X + 2 + 2X + 4 + 3X + 21 x 3X - 6

   = 4X + 6 + 3X + 21 x 3X - 6

   = 15X + 6 + 21 - 6

   = 15X + 27 - 6

   = 15X + 21

b) 5 (-2X + 3)(-2X + 1)- 2 (X + 1) ²

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

    = [5 x (-2X)] + [5 x 3] x [5 x (-2X)] + [5 x 1] - [(2 x X) + (2 x 1)]²

    = 10X + 15 x 10X + 5 - [2X + 2]²

    = 10X + 15 x 10X + 5 - [(2X + 2) x (2X + 2)]

    = 10X + 15 x 10X + 5 - [(2X x 2X) + (2X x 2) + (2 x 2X) + (2 x 2)

    = 10X + 15 x 10X + 5 - [2X² + 4X + 4X + 4]

    = 10X + 15 x 10X + 5 - [2X² + 8X + 4]