quel qu'un pouvez vous m'expliquer si'il vous plait ex1) A = ( x - 2 )² + (x - 2) (3x + 1) 1. Développer et réduire A. 2. Factoriser A. 3. Résoudre l'équation :

1) développer et réduire :
A = x^2 - 4x + 4 + 3x^2 + x - 6x - 2
A = 4x^2 - 9x + 2

2) factoriser :
A = (x - 2) (x - 2 + 3x + 1)
A = (x - 2) (4x - 1)

3) résoudre :
(x - 2) = 0
x = 2

4x - 1 = 0
4x = 1
x = 1/4

S = {1/4;2}

4) calcul pour x = -1/2
A = (-1/2 - 2)(4 * (-1/2) - 1)
A = (-1/2 - 4/2)(-2 - 1)
A = (-5/2)(-3)
A = 15/2

Exo 2 :

1) A = 49x - 42x + 9 - 9
A = 7x

2) A = (7x - 3 - 3)(7x - 3 + 3)
A = (7x - 6)(7x)
A = 7x (7x - 6)

3) 7x = 0
x = 0

7x - 6 = 0
7x = 6
x = 6/7

4) (7 * 2/3)(7 * 2/3 - 6) = 14/3 * (14/3 - 18/3)
= 14/3 * (-4/3)
= -56/9

Exo 3 :

1) A = 4x^2 - 12x + 9 - (8x^2 - 12x + 14x - 21)
A = 4x^2 - 12x + 9 - 8x^2 + 12x - 14x + 21
A = -4x^2 - 14x + 30
A = 2 (-2x^2 - 7x + 15)

2) A = (2x - 3)(2x - 3 - 4x - 7)
A = (2x - 3)(-2x - 10)
A = 2(2x - 3)(-x - 5)

3) 2x - 3 = 0
2x = 3
x = 3/2

-x - 5 = 0
x = -5

S = {-5;3/2}

4) A = (2 * 3/4 - 3)(-2 * 3/4 - 10)
A = (3/2 - 6/2)(-3/2 - 20/2)
A = (-3/2)(-23/2)
A = 69/4