Exercice 1 de la feuille ( en detaiilant ) , urgent !! merci d'avance

2
G=(9x-4)(3x-5)-(2x+8)(6-2x)
Developper , reduire et ordonner
Rappels :
k(a+b)=ka+kb k(a-b) = ka- kb (a+b)(c+d) = ac+ad+bc+bd
Utilise les identités remarquables.

Réponses

2013-10-05T17:11:21+02:00
A= 8x(1-7x)=8x-56x²
B= -9x(4-x)= -36x+9x²
C= (-7x+5)(2x+8)= -14x²-56x+10x+40= -14x²-46x+40
D= (6x-1)(5x+4)+9(2-7x)=(30x²+20x-5x-4)+18-63x=30x²-48x+14
E= (9-8x)(3x+5)-2x(4+11x)=(27x+45-24x²-40x)-8x-22x²=-46x²-21x+45
F=(6x-1)(4x+2)+(3-5x)(3x+4)=(24x²+12x-4x-2)+(9x+12-15x²-20x)=9x²-3x+10
G= (9x-4)(3x-5)-(2x+8)(6-2x)=(27x²-45x-12x+20)-(12x-4x²+48-16x)=27x²-57x+20-12x+4x²-48+16x=31x²-53x-28
2013-10-05T17:34:10+02:00
 Exercice 1 :
A = 8x ( 1 - 7x )
= 8x * 1 + 8x * 7x
8x + 56x^{2}

B = -9x ( 4 - x )
= -9x * 4 + (-9x) * x
= -36x - 9x

C = ( -7x + 5 ) ( 2x + 8 )
= -7x * 2x + (-7x) * 8 + 5 * 2x + 5 * 8
 -14x^{2} + (-56x) + 10x + 40
 -14x^{2} - 46x + 40

D = ( 6x - 1 ) ( 5x + 4 ) + 9 ( 2 - 7x )
= 6x * 5x + 6x * 4 + (-1) * 5x + (-1) * 4 + 9 * 2 + 9 * (-7x)
30x^{2} + 24x + (-5x) + (-4) + 18 + (-63x)
 30x^{2} - 44x + 14

E = ( 9 - 8x ) ( 3x + 5 ) - 2x ( 4 + 11x )
= 9 * 3x + 9 * 5 + (-8x) * 3x + (-8x) * 5 - 2x * 4 + (-2x) * 11x
= 27x + 45 + -24x^{2} + (-40x) - 8x + (-22 x^{2} )
= -21x -  46x^{4} + 45

F = ( 6x - 1 ) ( 4x + 2 ) + ( 3 - 5x ) ( 3x + 4 )
= 6x * 4x + 6x * 2 + (-1) * 4x + (-1) * 2 + 3 * 3x + 3 * 4 + (-5x) * 3x + (-5) * 4
 24x^{2} + 12x + (-4x) + (-2) + 9x + 12 + (15 x^{2} ) + (-20)
39 x^{4} + 17 - 8

G = ( 9x - 4 ) ( 3x - 5 ) - ( 2x + 8 ) ( 6 - 2x )
= 9x * 3x + 9x * (-5) + (-4) * 3x + (-4) * (-5) - 2x * 6 + 2x * (-2x) + 8 * 6 + 8 * (-2x)
 27x^{2} + (-45) + (-12x) + 20 - 12x + ( -4x^{2} ) + 48 + (-16x)
23 x^{4} + 23 - 40x

Exercice 2 :
1) D'après le théorème de Pythagore.
EF^{2} =  DF^{2} -  DE^{2}
 EF^{2} =  13^{2} -  12^{2}
 EF^{2} = 169 - 144 = 25
EF =  \sqrt{25} = 5cm

2) GHI est un triangle rectangle. ( Comment j'ai fais ? c'est simple, j'ai utiliser Pythagore )