Factorise les expressions suivantes a. (2x - 3)(x +2) - 5(2x - 3) b. (5x + 1)(3x - 5) - (x - 3)(5x + 1) c. (3x + 2)(-5x - 7) - (3x + 2)(x + 7) d. (5x - 8)(7x -

Bonjour

♤a.

A = (2x-3)(x+2)-5(2x-3)
A = (2x-3)[(x+2)-5]
A = (2x-3)(x-3)

♤b.

B = (5x+1)(3x-5)-(x-3)(5x+1)
B = (5x+1)[(3x-5)-(x-3)]
B = (5x+1)(2x-2)

♤c.

C = (3x+2)(-5x-7)-(3x+2)(x+7)
C = (3x+2)[(-5x-7)-(x+7)]
C = (3x+2)(-6x-14)

♤d.

D = (5x-8)(7x-3)-(7x-3)²
D = (7x-3)[(5x-8)-(7x-3)]
D = (7x-3)(-2x-5)

Voilà ^^

a)
(2x-3)(x+2)-5(2x-3)
=(2x-3)(x+2-5)
=(2x-3)(x-3)
b)
(5x+1)(3x-5)-(x-3)(5x+1)
=(5x+1)((3x-5)-(x-3))
=(5x+1)(3x-5-x+3)
=(5x+1)(2x-2)
c)
(3x+2)(-5x-7)-(3x+2)(x+7)
=(3x+2)((-5x-7)-(x+7))
=(3x+2)(-5x-7-x-7)
=(3x+2)(-6x-14)
d)
(5x-8)(7x-3)-(7x-3)²
=(5x-8)(7x-3)-(7x-3)(7x-3)
=(7x-3)((5x-8)-(7x-3))
=(7x-3)(5x-8-7x+3)
=(7x-3)(-2x-5)