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Exercice n°2 :
1°) Factoriser les deux expressions suivantes :
A = (5x – 2)(4x + 1) + (5x – 2)(x-6);
B=(7x-2)2 – (3x + 1)2 :
2°) On pose
C = (4x – 3)(2x +2) – 5(4x – 3).
a) Développer et réduire C.
b) Factoriser C.
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NADA247

Bonjour

Exercice 2:

1) Factoriser

A = (5x – 2)(4x + 1) + (5x – 2)(x-6)

= (5x - 2) (4x + 1 + x - 6)

= (5x - 2) (5x -5)

= (5x -2) 5(x - 1)

B = (7x-2)2 – (3x + 1)2

= 2[(7x - 2)-(3x + 1)]

= 2(7x - 3x - 2 - 1)

= 2(4x - 3)

2) On pose:

C = (4x – 3)(2x +2) – 5(4x – 3).

a) Développer et réduire C.

C = (4x – 3)(2x +2) – 5(4x – 3).

= 8x² + 8x - 6x - 6 - 20x + 15

= 8x² - 18x + 9

b) Factoriser C.

C = (4x – 3)(2x +2) – 5(4x – 3)

= (4x - 3) [(2x+2) -5]

= (4x -3 ) (2x + 2 - 5)

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