Bonsoir j’ai besoin d’aide pour la factorisation des exos 3 et 4

Bonjour

Exercice 3

a. (3x + 1) (2 - 2x) - (5 - 4x) (x - 1)
= (3x + 1) * (-2) (-1 + x) - (5 - 4x) (x - 1)
= -2 (3x + 1) (x - 1) - (5 - 4x) (x - 1)
= (x - 1) [ -2 (3x + 1) - (5 - 4x) ]
= (x - 1) [ (-6x - 2) - (5 - 4x) ]
= (x - 1) (-6x - 2 - 5 + 4x)
= (x - 1) (-2x - 7)

b. (2 - 3x) (3 + 2x) + (3x + 2) (-6x - 9)
= (2 - 3x) (3 + 2x) + (3x + 2) * (-3) (2x + 3)
= (2 - 3x) (3 + 2x) + (-3) (3x + 2) (3 + 2x)
= (3 + 2x) [ (2 - 3x) + (-3) (3x + 2) ]
= (3 + 2x) [ (2 - 3x) + (-9x - 6) ]
= (3 + 2x) (2 - 3x - 9x - 6)
= (3 + 2x) (-12x - 4)

c. (6x + 2) (2x + 3) + (9x + 3)²
= (6x + 2) (2x + 3) + (9x + 3) (9x + 3)
= 2 (3x + 1) (2x + 3) + 3 (3x + 1) (9x + 3)
= (3x + 1) [ 2 (2x + 3) + 3 (9x + 3) ]
= (3x + 1) [ (4x + 6) + (27x + 9) ]
= (3x + 1) (4x + 6 + 27x + 9)
= (3x + 1) (33x + 15)

d. (3x + 3)² - (x + 2) (5x + 4)
= (3x + 3) (3x + 3) - (x + 2) (5x + 4)
= 9x² + 18x + 9 - (5x² + 4x + 10x + 8)
= 9x² + 18x + 9 - 5x² - 14x - 8
= 4x² - 4x + 1                                            => identité remarquable du type
                                                                             a² - 2ab + 2² = (a - b)²
= (2x)² - 2 * 2x * 1 + 1²
= (2x - 1)²

Exercice 4

a. (2x - 4) (3x + 1) - (6x + 2) (4x + 1)
= (2x - 4) (3x + 1) - 2 (3x + 1) (4x + 1)
= (3x + 1) [ (2x - 4) - 2 (4x + 1) ]
= (3x + 1) [ (2x - 4) - (8x + 2) ]
= (3x + 1) (2x - 4 - 8x - 2)
= (3x + 1) (-6x - 6)

b. (2 - 6x) + (x + 1) (3x - 1)
=  -2 (-1 + 3x) + (x + 1) (3x - 1)
= -2 (3x - 1) + (x + 1) (3x - 1)
= (3x - 1) [ (-2) + (x + 1) ]
= (3x - 1) (-2 + x + 1)
= (3x - 1) (-1 + x)

c. (2x - 8) (7x + 1) - 16 + x²
= (2x - 8) (7x + 1) - (16 - x²)
= (2x - 8) (7x + 1) - (4² - x²)                 => identité remarquable du type a² - b²
                                                                              = (a - b) (a + b)
= (2x - 8) (7x + 1) - (4 - x) (4 + x)
= -2 (-x + 4) (7x + 1) - (4 - x) (4 + x)
= -2 (4 - x) (7x + 1) - (4 - x) (4 + x)
= (4 - x) [ -2 (7x + 1) - (4 + x) ]
= (4 - x) [ (-14x - 2) - (4 + x) ]
= (4 - x) (-14x - 2 - 4 + x)
= (4 - x) (-13x - 6)

Voilà j'espère avoir pu t'aider ^^
N'hésite pas si tu as des questions :)