Bonjour !
Exercice 1 :
A1 : (x + 2)² = x² + 4x + 4
A2 : (10t + 5)² = 100t² + 100t + 25
A3 : (y - 5)² = y² - 10y + 25
A4 : (3a - 7)² = 9a² - 42a + 49
A5 : (3y + 2)(3y - 2) = 9y² - 4
B1 : 2(3x - 4)² = 2(9x² - 24x + 16) = 19x² - 48x + 32
B2 : - (m + 7)² = -(m² + 14m + 49) = -m² - 14m - 49
B3 : -10(2a - 9)(2a + 9) = -10(40² - 81) = -400a² + 810
B4 : 7(3b - 1)² = 7(9b² - 6b + 1) = 63b² - 42b + 7
B5 : (x + 3)² + (2x + 7)² = x² + 6x + 9 + 4x² + 28x + 49 = 5x² + 64x + 58
C1 : (2x + 1)² - (3x - 2)(3x + 2) = 4x² + 4x + 1 - 9x² + 4 = -5x² + 4x + 5
C2 : (2y + 3)² - (2y + 3)(x - 7) = 4y² + 12y + 9 - 2yx - 3x + 14y + 21
= 4y² + 26y + 30 - 2yx - 3x
C3 : 3(7m - 4)² - (m + 2)² = 147m² - 168m + 48 - m² - 4m - 4 = 146m² - 172m + 44
C4 : (7x - 2)(3x + 1) - 2(2x + 1)² = 21x² - 6x + 7x - 2 - 8x² - 8x - 2 = 13x² - 7x - 4
C5 : 5(3t - 9)(3t + 9) - (3t + 4)² = 45t² - 405 - 9t² - 24t - 16 = 36t²- 421 - 24t
Exercice 2 :
A1 : 64x² - 49 = (8x - 7)(8x + 7)
A2 : (2x + 1)(3x + 5) + (4x + 2)(2x + 1) = (2x + 1)(3x+5+4x+2) = (2x + 1)(7x+7) = 7(2x+1)(x+1)
A3 : 16y² - 40y + 25 = (4y - 5)²
A4 : (t - 2)(t + 3) + (t - 2)(4t - 1) = (t - 2)(t + 3 + 4t - 1) = ((t - 2)(5t + 2)
A5 : x² + 4x + 4 = (x + 2)²
B1 : (7x + 3)(3x - 2) + 3x - 2 = (3x - 2)(7x + 3 + 1) = (3x - 2)(7x + 4)
B2 : (y + 5)² - 25 = (y + 5 + 5)(y + 5 - 5) = y(y + 10)
B3 : (6x - 1)(7x - 3) - (7x - 3)(x + 9) = (7x - 3)(6x - 1 - x - 9) = (7x - 3)(5x - 10) = 5(7x-3)(x-2)
B4 : 4(a - 5) - (a - 5)² = (a - 5)(4 - a + 5) = (a - 5)(9 - a)
B5 : (r + 8)(r + 7) - (2r + 5)(r + 8) = (r + 8)(r + 7 - 2r - 5) = (r + 8)(-r + 2)
C1 : 9x² - 16 + (3x + 4)(3x - 2) = (3x - 4)(3x + 4) + (3x + 4)(3x - 2) = (3x + 4)(3x - 4 + 3x - 2) = (3x + 4)(6x - 6) = 6(3x + 4)(x - 1)
C2 : (4x - 1)² - (x - 5)² = (4x - 1 - x + 5)(4x - 1 + x - 5) = (3x + 4)(5x - 6)
C3 : (7x - 5)(3x + 2) - 6(3x + 2)(x + 3) = (3x + 2)(7x - 5 - 6x - 18) = (3x + 2)(x - 23)
C4 : (2x + 3)(2x - 1) + 4x² + 12x + 9 = (2x + 3)(2x - 1) + (2x + 3)² = (2x + 3)(2x - 1 + 2x + 3)
= (2x + 3)(4x + 2) = 2(2x + 3)(2x + 1)
C5 : (6x - 1)² - (7x + 2)² = (6x - 1 - 7x - 2)(6x - 1 + 7x + 2) = (-x - 3)(13x + 1)
J'espère t'avoir aidé. Bon courage !
