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2013-12-20T17:19:51+01:00
Exercice 1
A = (4x+4)² -(-x-3)(5x-4)
A = 16x²+32x+16 -(-5x²+4x-15x+12)
A = 16x²+32x+16 -(-5x²-11x+12)
A = 16x²+32x+16 +5x²+11x-12
A = 21x²+43x+4

B = 4(3x+6)(5x+1)-2(3x-6)²
B = 4(15x²+3x+30x+6)-2(9x²-36x+36)
B = 4(15x²+33x+6)-2(9x²-36x+36)
B = 4(15x²+33x+6)-2(9x²-36x+36)
B = 60x²+132x+24-18x²+72x-72
B = 42x²+204x-48

C = (-2x+1)(x+3)-2(x-5)
C = -2x²-6x+x+3 -2x+10
C = -2x²-7x+13

D = 3(4x+3)(x+1)+(x+1)²
D = 3(4x²+4x+3x+3)+x²+2x+1
D = 12x²+21x+9+x²+2x+1
D = 13x²+23x+10

E = (3x-1)(2x+5)-3(x+1)(x-2)
E = 6x²+15x-2x-5 -3(x²-2x+x-2)
E = 6x²+13x-5 -3(x²-x-2)
E = 6x²+13x-5 -3x²+3x+6
E = 3x²+16x+1

Exercice 2
F = (8x-3)(8-7x)+(8x-3)(-x-9)
F = (8x-3)(8-7x-x-9)
F = (8x-3)(-8x-1)

G = (5x-9)²+(5x+10)(5x-9)
G = (5x-9)(5x-9)+(5x+10)(5x-9)
G = (5x-9)(5x-9+5x+10)
G = (5x-9)(10x+1)

H = (x+1)²+(x+1)
H = (x+1)(x+1)+(x+1)
H = (x+1)(x+1+1)
H = (x+1)(x+2)

I = 49x² - 9 identité remarquable de la forme a²-b² = (a+b)(a-b) avec a=7x et b=3
I = (7x+3)(7x-3)

J = (5x-2)² - 16 identité remarquable de la forme a²-b² = (a+b)(a-b) avec a=5x-2 et b=4
J = (5x-2+4)(5x-2-4)
J = (5x+2)(5x-6)

K = (3x-4)² - (5x-1)² identité remarquable de la forme a²-b² = (a+b)(a-b) avec a=3x-4 et b=5x-1
K = (3x-4+5x-1)(3x-4-(5x-1))
K = (3x-4+5x-1)(3x-4-5x+1)
K = (8x-5)(-2x-3)

L = x² - 25 + 2(x-5)(x+3)
or  x² - 25 identité remarquable de la forme a²-b² = (a+b)(a-b) avec a=x et b=5
x² - 25 = (x+5)(x-5)
on remplace dans L donc
L = (x+5)(x-5)+ 2(x-5)(x+3)
L = (x-5)(x+5+2(x+3))
L = (x-5)(x+5+2x+6)
L = (x-5)(3x+11)