Bonsoir je dois factoriser cette expression : E(x) = 9(x+1)² -25 (x-1)² Merci !

Bonsoir,

E(x) = 9(x + 1)² - 25(x - 1)²

E(x) = 3²(x + 1)² - 5²(x - 1)²

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

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

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

E(x) = 2(-x + 4) × 2(4x - 1)

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

Réponse :

Explications étape par étape

a^2 - b^2 = (a - b)(a + b)

Bonsoir

factoriser cette expression :

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)