Bonsoir,
Exercice 1
D = (3x + 1)(2x - 3) - (2x - 3)²
1) Factoriser D.
[tex]D = (3x + 1)(2x - 3) - (2x - 3)^2\\D = (3x + 1)(2x - 3) - (2x - 3)(2x-3)\\D =(2x - 3) [(3x + 1) - (2x - 3)]\\D =(2x - 3) (3x + 1 - 2x + 3)\\\boxed{D =(2x - 3) (x + 4)}[/tex]
2) D =(2x - 3) (x + 4)
Si x = -2, alors [tex]D =[2\times(-2) - 3] (-2 + 4)\\D =(-4 - 3) (-2 + 4)\\D=(-7)\times2\\\boxed {D=-14}[/tex]
Si x = 1,5, alors [tex]D =(2\times1,5 - 3) (1,5 + 4)\\D =(3 - 3) (1,5 + 4)\\D =0\times5,5\\\boxed{D=0}[/tex]
3) [tex]D =(2x - 3) (x + 4)\\D=2x\times x+2x\times4-3\times x-3\times4\\D=2x^2+8x-3x-12\\\boxed{D=2x^2+5x-12}[/tex]
Exercice 3
A = 36 - 25x²
A = 6² - (5x)²
A = (6 + 5x)(6 - 5x)
B = 100 + 60x + 9x²
B = 10² + 2*10*3x + (3x)²
B = (10 + 3x)²
C = b² - 10b + 25
C = b² - 2*b*5 + 5²
C = (b - 5)²
