EXERCICE 11 de la feuille des 17 ex
Développons, réduisons les expressions:
• A(x) = (2 x+3 ) ( x - 1) - 2 x ( x- 2 ) Réponse: A(x) = 5 x - 3
En effet :
A(x) = 2 x 2 + 3 x - 3 - 2 x - 2 x2 + 4 x = 2 x2 + 3x - 3 - 2 x - 2 x2 + 4 x = 5x - 3
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• B(x) = ( - 2 x + 3 )2 - 2 x 3x Réponse: B ( x ) = - 2 x2 - 12 x + 9
En effet:
B ( x ) = 4 x2 + 9 - 12 x - 6 x2 = - 2 x2 - 12 x + 9
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• C(x) = ( 2 x + 1 )2 + ( 3 x - 2 ) ( 3 x + 2 ) Réponse: C( x ) = 13 x2 + 4 x - 3
En effet:
C( x ) = 4 x2 + 1 + 4 x + 9 x2 - 4 = 13 x2 + 4 x - 3
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• D(x) = - ( - 3 x - 2 )2 + x ( 2 - x ) ( 3 + x ) Réponse : D(x) = - x 3 - 10 x2 - 6 x - 4
En effet:
D(x) = - ( 3 x + 2 )2 + ( 2 x - x2 ) (3 + x ) = - ( 9 x2 + 4 + 12 x ) + 6 x - 3 x2 - x3 + 2 x2
D(x) = - 9 x2 - 4 - 12 x + 6 x - 3 x2 - x3 + 2 x2 = - x3 - 10 x2 - 6 x - 4
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• E(x) = ( - 3 + 2 x) ( 3 + 2 x) Réponse: E( x ) = 4 x2 - 9
En effet:
E(x) =( 2 x - 3 ) ( 2 x + 3 ) = 4 x2 - 9
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