Réponse :
Explications étape par étape
Bonjour
Développer et réduire les expressions suivantes:
a) (x+2)*
= x^2 + 4x + 4
e) (7a+6b)*
= 49a^2 + 84ab + 36b^2
b) (x-8)*
= x^2 - 16x + 64
f) (2y+9)(2y-9)
= 4y^2 - 81
c) (x-5)(x+5)
= x^2 - 25
g) (6x-5)*+(7x-2)(x+3)
= 36x^2 - 60x + 25 + 7x^2 + 21x - 2x - 6
= 43x^2 - 41x + 19
d) (3x-4)*
= 9x^2 - 24x + 16
h) 7(2x-1)-(8x+2)+(x-3)
= 14x - 7 - 8x - 2 + x - 3
= 7x - 12
exercice 2
factoriser les expressions suivantes :
i) 4x*-6x+2.
= (2x)^2 - 2 * 2x * 3/2 + (3/2)^2 - (3/2)^2 + 2
= (2x - 3/2)^2 - 9/4 + 8/4
= (2x - 3/2)^2 - 1/4
= (2x - 3/2)^2 - (1/2)^2
= (2x - 3/2 - 1/2)(2x - 3/2 + 1/2)
= (2x - 4/2)(2x - 2/2)
= (2x - 2)(2x - 1)
= 2(x - 1)(2x - 1)
j) 45xy*+15xy*-20xy
= 5xy(9y + 3y - 4)
= 5xy(12y - 4)
= 20xy(3y - 1)
k) (x+2)(5x-1)+(x+2)(8x+3)
= (x + 2)(5x - 1 + 8x + 3)
= (x + 2)(13x + 2)
l) (x+1)*-64
= (x + 1)^2 - 8^2
= (x + 1 - 8)(x + 1 + 8)
= (x - 7)(x + 9)
m) (2x-1)*-(4x+9)*
= (2x - 1 - 4x - 9)(2x - 1 + 4x + 9)
= (-2x - 10)(6x + 8)
= (-2)(x + 5) * 2(3x + 4)
= (-4)(x + 5)(3x + 4)
n) 49y*-1-(2y-3)(7y-1)
= (7y)^2 - 1^2 - (2y - 3)(7y - 1)
= (7y - 1)(7y + 1) - (2y - 3)(7y - 1)
= (7y - 1)(7y + 1 - 2y + 3)
= (7y - 1)(5y + 4)
