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Bonjour pouvez vous m'aidez

Factoriser les exercices suivants
A = 25x2 – 49 ; B = (4x – 3)2 – 64 ; C = 9 – 36x2 ; D = (x – 1)2 – (5x + 3)2
E = 16x2 – (3x + 5)2 ; F = (2x + 7) (5x – 3) + (3x + 8) (2x + 7) ; G = (2x + 5) (x – 6) – (x – 6)2
H = 9x2 – 27x + 9 ; I = (5x – 3) (x – 1) – (x – 1) (6x – 5) ; J = (2x – 3)2 – 100
K = (3x + 5) (8x – 6) – (3x + 5)2 ; L = (4x – 3)2 – (2x – 9)2 ; M = 14x2 – 21xy + 7x

Sagot :

Réponse :

Explications étape par étape

  forme a²-b² =  (a+b) (a-b)

A = 25x²-49 = (5x+7) (5x-7)

B = (4x-3)² -64 = (4x-3+8) (4x-3-8) = (4x+5) (4x-11)

C =  (9 -36x²) = (3-6x) (3+6x) = (-6x+3) (6x+3)

D = (x-1)² -(5x+3)² = (x-1 +5x+3) (x-1 -5x-3) = (6x+2) (-4x-4)

E =  16x²-(3x+5)² = (4x+3x+5) (4x-3x-5) = (7x+5)(x-5)

F = (2x+7) ( (5x-3) + (3x+8) ) = (2x+7) (8x+5)

G = (x-6) .( ( 2x+5) -2) = (x-6) (2x+3)

H = 9x²-27x+9 = 9(x²-3x+1)

complétion de carré

   =9(x²-3x+9/4 -9/4 +1)

   = 9( ( x - 3/2 )² -5/4 )

   = 9( ( x-3/2)+√5/4) ( (x-3/2) -√5/4) )

I = (x-1) ( (5x-3)- (6x-5) ) = (x-1 ) ( -x+2)

J = (2x-3)² -100 = (  (2x-3) +10) ((2x-3) -10) = (2x+7) ( 2x-13)

K = (3x+5) ( ( 8x-6) -2) = (3x+5) ( 8x-8)

L = (4x-3)² - (2x-9)² = (4x-3+2x-9) (4x-3-2x+9) = (6x-12) (2x+6)

M = 14x² -21xy +7x = 7x(2x-3y+1)

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