Bonjour, j'aimerais avoir de l'aide pour un exercice svp Exercice : Soit H(x)=(x+2)² - (5x-1)(x+2) 1. Développer puis réduire H(x) 2. Factoriser H(x) 3. Repren

1)H(x)=(x^2+4x+4)-(5x^2+10x-x-2)
=x^2+4x-4-5x^2-9x+2
=-4x^2-5x-2
2) H(x)=(x+2)^2-(5x-1)(x+2)
=(x+2)((x+2)-(5x-1))
=(x+2)(x+2-5x+1)
=(x+2)(-4x+3)
3)K(x)=(x-1)(x+1)-(x-1)^2
=(x^2-1)-(x^2+1-2x)
=x^2-1-x^2-1+2x
=2x-2
=2(x-1) ---> forme developpee

K(x)=(x-1)(x+1)-(x-1)^2
=(x-1)((x+1)-(x-1))
=(x-1)(x+1-x+1)
=(x-1)(2)
=2(x-1) ----> forme factorisee

1/
H(x) = (x+2)² - (5x-1)(x+2)
H(x) = (x² + 4x +4) - (5x² + 10x - x - 2)
H(x) = x² + 4x +4 - 5x² - 10x + x + 2
H(x) = - 4x²  - 5x + 6


2/
H(x) = (x+2)² - (5x-1)(x+2)
H(x) = ((x+2) - (5x-1))(x+2)
H(x) = (x + 2 - 5x + 1)(x+2)
H(x) = ( - 4x + 3) (x+2)


3/
K(x)=(x-1)(x+1)-(x-1)²

a- Développer puis réduire K(x)
K(x)=(x-1)(x+1)-(x-1)²
K(x)=(x² -x + x - 1) - ( x² - 2x + 1)
K(x)=(x² -x + x - 1) - ( x² - 2x + 1)
K(x)=(x² - 1) - x² + 2x - 1
K(x)=x² - 1 - x² + 2x - 1
K(x)= 2x - 2


b- Factoriser K(x)
K(x)=(x-1)(x+1)-(x-1)²
K(x)=(x-1) ((x+1)-(x-1))
K(x)=(x-1) (x+1- x + 1)
K(x)=(x-1) ( 1 + 1)
K(x)=(x-1) 2
K(x)= 2 (x-1)