SOS identités remarquables : factoriser les expressions

A = (x² - 6x + 9) - (x - 3) (3x + 4)

B = (16x² - 9) + (4x - 3) (5x + 4) - 16x² - 24x + 9)

C = (4x² + 4x + 1) - 3 (x + 2) '2x + 1) + (2x + 1)

Merci d'avance

Kévin

2

Réponses

2014-02-01T13:44:44+01:00
Bonjour

A =  (x² - 6x + 9) - (x - 3) (3x + 4)
A = (x -3)² - (x-3)(3x+4)
A = (x-3)(x-3) - (3x+4)
A = (x-3)(x-3x -3x -4) = (x-3)( x-4)

  B = (16x² - 9) + (4x - 3) (5x + 4) - 16x² - 24x + 9)
(4x -3(4x +3) + (4x-3)(5x+4) - (4x -3)(4x-3)
(4x-3)(4x+3)+ (5x +4 ) = (4x-3)(4x+3 +5x +4) = (4x -3)( 9x +7)

  C = (4x² + 4x + 1) - 3 (x + 2) '2x + 1) + (2x + 1)
= (2x +1) ²- 3 (x+2) (2x+1) + (2x +1)
= (2x+1)(2x+1) - (3x +6)
= (2x+1)(2x+1 -3x -6)
= (2x+1)( -x -5)


2014-02-01T13:46:51+01:00
A=(x²-6x+9)-(x-3)(3x+4) 
=(x-3)²-(x-3)(3x+4)
=(x-3)(x-3-3x-4)
=(x-3)(-2x-7)

B=(16x²-9)+(4x-3)(5x+4)-(16x²-24x+9) 
=(4x-3)(4x+3)+(4x-3)(5x+4)-(4x-3)²
=(4x-3)(4x+3+5x+4-4x+3)
=(4x-3)(5x+10)
=5(4x-3)(x+2)

C= (4x²+4x+1)-3(x+2)(2x+1)+(2x+1) 
=(2x+1)²-3(2x+1)(2x+1)+(2x+1) 
=(2x+1)(2x+1-3(2x+1)+1)
=(2x+1)(2x+1-6x-3+1)
=(2x+1)(-4x-1)