Bonjour,
Pour tes exercices, il faut utiliser les identités remarquables:
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
(a + b)(a - b) = a² - b²
Exercice 55 :
A = (6 + x)²
A = 6² + 2*6*x + x²
A = x² + 12x + 36
B = (6 - x)²
B = 6² - 2*6*x + x²
B = x² - 12x + 36
C = (6 * x)²
C = (6x)²
C = 36x²
D = (3 + x)²
D = 3² + 2*3*x + x²
D = x² + 6x + 9
E = (3 - x)²
E = 3² - 2*3*x + x²
E = x² - 6x + 9
F = (3 * x)²
F = (3x)²
F = 9x²
Exercice 56 :
G = (5 + 3x)²
G = 5² + 2*5*3x + (3x)²
G = 9x² + 30x + 25
H = (5 - 3x)²
H = 5² - 2*5*3x + (3x)²
H = 9x² - 30x + 25
I = (5 * 3x)²
I = (15x)²
I = 225x²
J = (4 + 2x)²
J = 4² + 2*4*2x + (2x)²
J = 4x² + 16x + 16
K = (4 - 2x)²
K = 4² - 2*4*2x + (2x)²
K = 4x² - 16x + 16
L = (4 * 2x)²
L = (8x)²
L = 64x²
Exercice 62 :
Ici, il faut utiliser la double distributivité :
(a + b)(c + d) = ac + ad + bc + bd
A = (2x + 5)(2x - 5)
A = 2x * 2x - 2x*5 + 5*2x - 5*5
A = 4x² - 10x + 10x - 25
A = 4x² - 25
B = (x - 3)(x + 3)
B = x*x + 3*x - 3*x - 3*3
B = x² + 3x - 3x - 9
B = x² - 9
C = (5a + 2)(5a - 2)
C = 5a*5a - 5a*2 + 2*5a - 2*2
C = 25a² - 10a + 10a - 4
C = 25a² - 4
D = (3 + 5b)(3 - 5b)
D = 3*3 - 3*5b + 5b*3 - 5b*5b
D = 9 - 15b + 15b - 25b²
D = -25b² + 9
Exercice 66 :
A = (5x + 7)²
A = 5x*5x + 2*5x*7 + 7²
A = 25x² + 70x + 49
B = (4x - 3)(6x + 2)
B = 4x*6x + 4x*2 - 3*6x - 3*2
B = 24x² + 8x - 18x - 6
B = 24x² - 10x - 6
C = (2 - 6x)²
C = 2² - 2*2*6x + (6x)²
C = 36x² - 24x + 4
D = (9x - 3)(9x + 3)
D = 9x*9x + 9x*3 - 3*9x - 3*3
D = 81x² + 27x - 27x - 9
D = 81x² - 9
E = (1 + 2x)²
E = 1² + 2*1*2x + (2x)²
E = 4x² + 4x + 1
F = (4 - 7x)(4 + 7x)
F = 4*4 + 4*7x - 7x*4 - 7x*7x
F = 16 + 28x - 28x - 49x²
F = -49x² + 16
