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Exercice 2

Factoriser les expressions suivantes.

A = -(3x + 5) + (3x – 8) (3 x + 5)
B = 100.x2 – 81 – (10x + 9) (2 x – 10)
C = 100 x2 – 36
D=81 – (5 x – 1)2
E = (8x – 3)(-73 – 7) +(-73 – 7)?
F=-(6 x – 10) (-6x +10)+(-6x + 10) (2 – 10)

Exercice 3

Factoriser les expressions suivantes.

A= (-3x + 3)2 – 1
B = (9x— 7)(-10x+1)+(-10x+10)(-10x+1)
C = 4x2 – 36 – (2x+6)(-3x – 9)
D = 49x2 – 36
E = (10x – 7) – (10 - 6) (10 3 – 7)
F=(-2x – 10)2 + (-2x – 10) (9.2 – 4)

Merci d'avance ​

Sagot :

Réponse :On factorise les expressions suivantes:

Ex 2

A = -(3x + 5) + (3x – 8) (3 x + 5)                facteur commun (3x +5)

A = (3x + 5)[(3x +8) -1]

A = (3x +5)(3x +7)

B = 100.x2 – 81 – (10x + 9) (2 x – 10)

B = (10x)² - 9² - (10x + 9) (2 x – 10)

B = (10x - 9)(10x + 9) -  (10x + 9) (2 x – 10)

B = (10x +9) [10x - 9 - (2x -10)]

B = (10x +9)(10x - 9 -2x + 10)

B = (10x + 9)(8x + 1)

C = 100 x2 – 36

C=  (10x)² - 6²

C = (10x - 6)(10x +6)

D=81 – (5 x – 1)2

D = 9² - (5x -1)²

D = (9 - (5x -1))(9 +(5x - 1)

D = (9 -5x +1)(8 +5x)

D = (10 - 5x)(8 + 5x)

E = (8x – 3)(-73x – 7) +(-73x – 7)²

E = (-73x - 7)(8x -3 - 73x - 7)

E = (-73x - 7)(-65x - 10)

F=-(6 x – 10) (-6x +10)+(-6x + 10) (2x – 10)

F = (-6x + 10) (-6x +10)+(-6x + 10) (2x – 10)

F = (-6x + 10)[(-6x + 10) + 2x -10]

F = -4x(-6x + 10)

Ex 3

A= (-3x + 3)² – 1

A = (-3x + 3)² – 1 ²

A = (-3x + 3 - 1)(-3x + 3 + 1)

A = (-3x + 2)(-3x + 4)

B = (9x— 7)(-10x+1)+(-10x+10)(-10x+1)

B = (-10x +1)(9x - 7 -10x + 10)

B = (-10x +1)(-x + 3)

C = 4x2 – 36 – (2x+6)(-3x – 9)

C = (2x)² - 6² - (2x+6)(-3x – 9)

C = (2x - 6)(2x +6) - (2x +6)(-3x - 9)

C = (2x + 6)[2x - 6 -(-3x -9)]

C = (2x + 6)(2x - 6 + 3x + 9)

C = (2x +6)(5x + 3)

D = 49x2 – 36

D = (7x)² - 6²

D = (7x - 6)(7x +6)

E = (10x – 7) – (10x - 6) (10x – 7)

E = (10x -7)[ 1 -(10x -6)]

E = (10x -7)(7 - 10x)

E = -(7 - 10x)(7 - 10x)

E = -(7 - 10x)²

F=(-2x – 10)² + (-2x – 10) (9x – 4)

F = (-2x -10)[(-2x - 10) + (9x - 4)]

F = (-2x - 10)(7x -14)

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