Explications étape par étape:

Pour simplifier ces expressions, développons-les :

1. a(x) = (x + 2)(x - 3) - (x + 2)²

a(x) = x² - 3x + 2x - 6 - (x² + 4x + 4)

a(x) = x² - x - 6 - x² - 4x - 4

a(x) = -5x - 10

2. b(x) = (2x + 3)² + (x - 5)(2x + 3)

b(x) = 4x² + 12x + 9 + 2x² - 10x + 3

b(x) = 6x² + 2x - 6

3. a(x) = (7x + 3)(4x - 1) + 3(4x - 1)(2x + 1)

a(x) = 28x² - 7x + 12x - 3 + 24x² - 6x + 12x + 3

a(x) = 52x²

4. b(x) = (3x + 5)(-x + 2) - 4(3x + 5)(4x + 1)

b(x) = -3x² + 6x - 15 - 12x² - 20x - 20

b(x) = -15x² - 14x - 35

5. a(x) = 5(x + 2) - 2(x + 1)(x + 2)

a(x) = 5x + 10 - 2(x² + 3x + 2)

a(x) = 5x + 10 - 2x² - 6x - 4

a(x) = -2x² - x + 6

6. b(x) = 2(-x + 5)(-x + 6) - 3(-x + 5)(2x + 3)

b(x) = 2(x - 5)(x - 6) - 3(2x² + 3x - 10x - 15)

b(x) = 2(x² - 11x + 30) - 6x² - 9x + 30

b(x) = 2x² - 22x + 60 - 6x² - 9x + 30

b(x) = -4x² - 31x + 90

Donc, les expressions simplifiées sont :

1. a(x) = -5x - 10

2. b(x) = 6x² + 2x - 6

3. a(x) = 52x²

4. b(x) = -15x² - 14x - 35

5. a(x) = -2x² - x + 6

6. b(x) = -4x² - 31x + 90