Exercice 1 :
A = 8x ( 1 - 7x )
= 8x * 1 + 8x * 7x
8x + [tex]56x^{2} [/tex]
B = -9x ( 4 - x )
= -9x * 4 + (-9x) * x
= -36x - 9x
C = ( -7x + 5 ) ( 2x + 8 )
= -7x * 2x + (-7x) * 8 + 5 * 2x + 5 * 8
= [tex] -14x^{2} [/tex] + (-56x) + 10x + 40
= [tex] -14x^{2} [/tex] - 46x + 40
D = ( 6x - 1 ) ( 5x + 4 ) + 9 ( 2 - 7x )
= 6x * 5x + 6x * 4 + (-1) * 5x + (-1) * 4 + 9 * 2 + 9 * (-7x)
= [tex]30x^{2} [/tex] + 24x + (-5x) + (-4) + 18 + (-63x)
= [tex] 30x^{2} [/tex] - 44x + 14
E = ( 9 - 8x ) ( 3x + 5 ) - 2x ( 4 + 11x )
= 9 * 3x + 9 * 5 + (-8x) * 3x + (-8x) * 5 - 2x * 4 + (-2x) * 11x
= 27x + 45 + [tex]-24x^{2} [/tex] + (-40x) - 8x + [tex](-22 x^{2} )[/tex]
= -21x - [tex] 46x^{4} [/tex] + 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
= [tex] 24x^{2} [/tex] + 12x + (-4x) + (-2) + 9x + 12 + [tex](15 x^{2} )[/tex] + (-20)
= [tex]39 x^{4} [/tex] + 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)
= [tex] 27x^{2} [/tex] + (-45) + (-12x) + 20 - 12x + [tex]( -4x^{2} )[/tex] + 48 + (-16x)
= [tex]23 x^{4} [/tex] + 23 - 40x
Exercice 2 :
1) D'après le théorème de Pythagore.
[tex]EF^{2} = DF^{2} - DE^{2} [/tex]
[tex] EF^{2} = 13^{2} - 12^{2} [/tex]
[tex] EF^{2} = 169 - 144 = 25 [/tex]
[tex]EF = \sqrt{25} = 5cm [/tex]
2) GHI est un triangle rectangle. ( Comment j'ai fais ? c'est simple, j'ai utiliser Pythagore )
