Exercice 1A.3 :
A = (3 + x)²
A = 3² + 2 * 3 * x + x²
A = x² + 6x + 9
B = (x + 5)²
B = x² + 2 * x * 5 + 5²
B = x² + 10x + 25
C = (2x + 1)²
C = (2x)² + 2 * 2x * 1 + 1²
C = 4x² + 4x + 1
D = (1 + 3x)²
D = 1² + 2 * 1 * 3x + (3x)²
D = 9x² + 6x + 1
E = (3x + 2)²
E = (3x)² + 2 * 3x * 2 + 2²
E = 9x² + 12x + 4
F = (5x + 3)²
F = (5x)² + 2 * 5x * 3 + 3²
F = 25x² + 30x + 9
G = (x² + 1)²
G = (x²)² + 2 * x² * 1 + 1²
G = x⁴ + 2x² + 1
H = (3 + 4x)²
H = 3² + 2 * 3 * 4x + (4x)²
H = 16x² + 24x + 9
Exercice 1A.4 :
A = (x - 2)²
A = x² - 2 * x * 2 + 2²
A = x² - 4x + 4
B = (1 - 3x)²
B = 1² - 2 * 1 * 3x + (3x)²
B = 9x² - 6x + 1
C = (3 - x)²
C = 3² - 2 * 3 * x + x²
C = x² - 6x + 9
D = (2x - 1)²
D = (2x)² - 2 * 2x * 1 + 1²
D = 4x² - 4x + 1
E = (3 - 5x)²
E = 3² - 2 * 3 * 5x + (5x)²
E = 25x² - 30x + 9
F = (3x - 2)²
F = (3x)² - 2 * 3x * 2 + 2²
F = 9x² - 12x + 4
G = (4x - 3)²
G = (4x)² - 2 * 4x * 3 + 3²
G = 16x² - 24x + 9
H = (4 - 3x²)²
H = 4² - 2 * 4 * 3x² + (3x²)²
H = 9x⁴ - 24x² + 16