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Sagot :

Bonsoir,

E = (3x + 2)² - (5 - 2x)(3x + 2)

1) E = (9x² + 12x + 4) - (15x + 10 - 6x² - 4x)

E = 9x² + 12x + 4 - 15x - 10 + 6x² + 4x

E = 15x² + x - 6

2) E = (3x + 2)² - (5 - 2x)(3x + 2)

E = (3x + 2)*(3x + 2) - (5 - 2x)(3x + 2)

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

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

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

3) Si x = -2, alors E = [3 * (-2) + 2][5 * (-2) - 3]

E = (-6 + 2)(-10 - 3)

E = (-4) * (-13)

E = 52

ou  E = [3 * (-2) + 2]² - [5 - 2 * (-2)][3 * (-2) + 2]

E = (-6 + 2)² - (5 + 4)(-6 + 2)

E = (-4)² - 9 * (-4)

E = 16 + 36

E = 52
DROOPETTE
On considère l'expression suivante : E= (3x+2)²- (5-2x)(3x+2)
1) Développer et réduire E
E= (3x+2)²- (5-2x)(3x+2)
=9x²+12x+4-(15x+10-6x²-4x)
=9x²+12x+4-15x-10+6x²+4x
=15x²+x-6

2) Factoriser E
E= (3x+2)²- (5-2x)(3x+2)
=(3x+2)(3x+2)- (5-2x)(3x+2)
=(3x+2)((3x+2-5+2x)
=(3x+2)(5x-3)

3) Calculer E pour x= -2
E(-2)=15x²+x-6
=15*(-2)²+(-2)-6
=15*4-2-6
=60-8
=52

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