Exercice 1
1) Développer les produits. 10(a+b) -5(3a-2b) 7(2x-3) 2)
Supprimer les parenthèses dans les expressions suivantes.
A = a - (b-c-d + e) B= (x + y) - (a - b) + (- d+ 1)
Exercice 2
Développer et réduire les produits suivants. A = (x+2) (x+5) B = (3x-7) (5x-2) C = (x+3) (4- x) D = (4x-5) (4x + 5) E = (2x +3)²
Exercice 3 Série d'exercices 1
1)Factoriser les sommes suivantes. A = (x-3) (x-1) + (x-3) (x-5) B = (4x-3) (x-1) -(4x-3) (2x+1) C=(x+1)2 +(x+1)(5x-3) D = (2x-1) ² (1-x) (2x-1) E = (2x-1)² - 5(2x-1) F = (x-1) (x+3) - 2(x+3)² G=x² + 2x (3x + 4)
2) Factoriser les sommes suivantes 10a 10b 5a + 35 7a + a -a - a 3x² + x x² +3 x F= (4 - 3x)² G= (2x + 1)² + (4x-3) (5x + 2) H = (x+1)² -(x+1) (3x-5) I=2-3x (5x +1) J = (2-3x) (5x +1) K = x²(x + 1) (x-1)
2) Factoriser en utilisant une identité remarquable. A = x² + 2x + 1 B= x² - 2x + 1 C=x²-1 D = 25x² + 40 x + 16 E = 4x² + 4x +1 F = 49x² 100
Aidez ma petite soeur, s'il vous plaît 8(
1) Développer les produits. 10(a+b) -5(3a-2b) 7(2x-3) 2)
Supprimer les parenthèses dans les expressions suivantes.
A = a - (b-c-d + e) B= (x + y) - (a - b) + (- d+ 1)
Exercice 2
Développer et réduire les produits suivants. A = (x+2) (x+5) B = (3x-7) (5x-2) C = (x+3) (4- x) D = (4x-5) (4x + 5) E = (2x +3)²
Exercice 3 Série d'exercices 1
1)Factoriser les sommes suivantes. A = (x-3) (x-1) + (x-3) (x-5) B = (4x-3) (x-1) -(4x-3) (2x+1) C=(x+1)2 +(x+1)(5x-3) D = (2x-1) ² (1-x) (2x-1) E = (2x-1)² - 5(2x-1) F = (x-1) (x+3) - 2(x+3)² G=x² + 2x (3x + 4)
2) Factoriser les sommes suivantes 10a 10b 5a + 35 7a + a -a - a 3x² + x x² +3 x F= (4 - 3x)² G= (2x + 1)² + (4x-3) (5x + 2) H = (x+1)² -(x+1) (3x-5) I=2-3x (5x +1) J = (2-3x) (5x +1) K = x²(x + 1) (x-1)
2) Factoriser en utilisant une identité remarquable. A = x² + 2x + 1 B= x² - 2x + 1 C=x²-1 D = 25x² + 40 x + 16 E = 4x² + 4x +1 F = 49x² 100
Aidez ma petite soeur, s'il vous plaît 8(
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1)
A = (x+2) (x+5)
= x(x+5) + 2(x+5)
= x² + 5x + 2x + 10
= x² + 7x + 10
B = (3x-7) (5x-2)
= 3x(5x-2) - 7(5x-2)
= 15x² - 6x - 35x + 14
= 15x² - 41x + 14
C = (x+3) (4- x)
= x(4-x) + 3(4-x)
= 4x - x² + 12 - 3x
= -x² + x + 12
D = (4x-5) (4x + 5)
= 4x(4x+5) - 5(4x+5)
= 16x² + 20x - 20x - 25
= 16x² - 25
E = (2x +3)²
= (2x +3)(2x +3)
= 4x² + 6x + 6x + 9
= 4x² + 12x + 9
2)
A = (x-3) (x-1) + (x-3) (x-5)
= (x-3)(x-1+x-5)
= (x-3)(2x-6)
= 2(x-3)x-6
B = (4x-3) (x-1) -(4x-3) (2x+1)
= (4x-3)(x-1-2x-1)
= (4x-3)(-x-2)
= - (4x-3)(x+2)
C = (x+1)² +(x+1)(5x-3)
= (x+1)(x+1+5x-3)
= (x+1)(6x-2)
= 2(x+1)3x-1
D = (2x-1)² (1-x) (2x-1)
= (2x-1)(2x-1)(1-x)
= (2x-1)²(1-x)
E = (2x-1)² - 5(2x-1)
= (2x-1)(2x-1) - 5(2x-1)
= (2x-1)(2x-1-5)
= (2x-1)(2x-6)
F = (x-1) (x+3) - 2(x+3)²
= (x-1)(x+3-2(x+3))
= (x-1)(-x-3)
= - (x-1)(x+3)
G = x² + 2x (3x + 4)
= x² + 6x² + 8x
= 7x² + 8x
= x(7x + 8)
3)
A = (x-3)(x-1) + (x-3)(x-5)
= (x-3)(x-1+x-5)
= (x-3)(2x-6)
= 2(x-3)(x-3)
B = (4x-3)(x-1) - (4x-3)(2x+1)
= (4x-3)(x-1-2x-1)
= (4x-3)(-x-2)
C = (x+1)^2 + (x+1)(5x-3)
= (x+1)(1+x+5x-3)
= (x+1)(6x-2)
= 2(x+1)(3x-1)
D = (2x-1)² (1-x)(2x-1)
= (2x-1)(2x-1)(1-x)
= (2x-1)² (1-x)
E = (2x-1)² - 5(2x-1)
= (2x-1)(2x-1-5)
= (2x-1)(2x-6)
F = (x-1)(x+3) - 2(x+3)²
= (x+3)(x-1-2(x+3))
= (x+3)(-3x-7)
= - (3x+7)(x+3)
G = x² + 2x(3x+4)
= x(x+2)(3x+4)
4)
a) 10a = 2a5
10b = 25b
factorisation commune : 25(a+b)
b) 5a+35 = 5(a+7)
c) 7a + a -a -a = 6a
d) x(3x+1) + 3(3x+1) = (3x+1)(x+3)
e) x²+3x = x(x+3)
x²+3 = (x+1)(x+3)
f) F= (4 - 3x)² = (2 - (3x))²
identité remarquable (a-b)² = a² - 2ab + b²
F = 4² - 243x + (3x)²
= 16 - 24x + 9x²
g) G= (2x + 1)² + (4x-3)(5x + 2)
identité remarquable (a+b)² = a² + 2ab + b²
G = (2x+1)² + (4x-3)(5x+2)
= (2x+1)² + 20x² - 7x - 6
= 4x² + 4x + 1 + 20x² - 7x - 6
= 24x² - 3x - 5
H = (x+1)² - (x+1) (3x-5)
= (x+1) (x+1) - (x+1) (3x-5)
= (x+1) [(x+1) - (3x-5)]
= (x+1) [x+1 - 3x + 5]
= (x+1) (-2x + 6)
= 2(x+1) (3-x)
i) I = 2 - 3x (5x + 1) = -(3x-1)(5x+1) + 3
j) J = (2-3x)(5x+1) = -(3x-1)(5x+1)
k) K = x²(x+1)(x-1) = x(x+1)(x-1)x
5)
a) x² + 2x + 1 = (x+1)²
b) x² - 2x + 1 = (x-1)²
c) x² - 1 = (x-1)(x+1)
d) 25x² + 40x + 16 = (5x+4)²
e) 4x² + 4x + 1 = (2x+1)²
f) 49x² - 100 = (7x-10)(7x+10)