Bonsoir il me reste des exos sur la factorisation : Factoriser les expressions suivantes : B(x) = (x-3)² - 25 C(x) = (2x -3)² - (x+7)² D(x) = 9(5x+1)² - (x+1)²

Réponse :

Explications étape par étape

a^2 - b^2 = (a - b)(a + b) => identité remarquable

Bonjour

factoriser :

B(x) = (x-3)² - 25

B = (x - 3)^2 - 5^2

B = (x - 3 - 5)(x - 3 + 5)

B = (x - 8)(x + 2)

C(x) = (2x - 3)² - (x+7)²

C = (2x - 3 - x - 7)(2x - 3 + x + 7)

C = (x - 10)(3x + 4)

D(x) = 9 (5x+1)² - (x+1)²

D = 3^2(5x + 1)^2 - (x + 1)^2

D = [3(5x + 1) - x - 1][3(5x + 1) + x + 1]

D = (15x + 3 - x - 1)(15x + 3 + x + 1)

D = (14x + 2)(16x + 4)

D = 2(7x + 1) * 4(4x + 1)

D = 8(7x + 1)(4x + 1)

E(x) = 9 (x+1)² - 25 (x-1)²

E = 3^2(x + 1)^2 - 5^2(x - 1)^2

E = [3(x + 1) - 5(x - 1)][3(x + 1) + 5(x - 1)]

E = (3x + 3 - 5x + 5)(3x + 3 + 5x - 5)

E = (-2x + 8)(8x - 2)

E = 2(-x + 4) * 2(4x - 1)

E = 4(-x + 4)(4x - 1)