Bonjour besoin d’aide et explication merci

Bonsoir,

1) (3x-5)(2x+1)

= 3x*2x + 3x*1 - 5*2x - 5*1

= 6x² + 3x - 10x - 5

= 5x² - 7x - 5

2) 4x(5-x) + (x+1)(x-1)

= 4(x*5) + x*(-x) + x*x + x*(-1) + 1*x - 1*1

= 4*5x - x² + x² - x + x - 1

= 20x - x + x - 1

= 20x - 1

3) 2(x-2)² + (2x+1)²

= 2(x² - 2 * x  * 2 + 2²) + ((2x)² + 2*2x*1 + 1²)

= 2(x² - 4x + 4) + (4x² + 4x + 1)

= 2*x² + 2*(-4x) + 2*4 + 4x² + 4x + 1

= 2x² - 8x + 8 + 4x² + 4x + 1

= 6x² - 4x + 9

4) (2x-1)x - 4x(4x+4)

= x*2x + x*(-1) - 4(x*4x + x*4)

= 2x² - x - 4(4x² + 4x)

= 2x² - x - 16x² - 16x

= -14x² - 17x

= x(-14x - 17)

5) (2x+2)(x+1) - 4(x+1)

= 2x*x + 2x*1 + 2*x + 2*1 - 4*x - 4*1

= 2x² + 2x + 2x + 2 - 4x - 4

= 2x² + 4x - 4x + 2 - 4

= 2x² - 2 ← Identité remarquable a² - b²

= 2(x+1)(x-1)

6) 2x³ - 4x² + 5x

= x(2x² - 4x + 5)

7) 5 - 8x = 14 - 12x

5 - 14 = -12x + 8x

-9 = -4x

x = [tex]\frac{-9}{-4}[/tex] = [tex]\frac{9}{4}[/tex] = 2.25

8) [tex]\frac{x}{2}[/tex] - [tex]\frac{5}{4}[/tex] = 4x - 2

[tex]\frac{x}{2}[/tex] - 4x = -2 + [tex]\frac{5}{4}[/tex]

0.5x - 4x = -2 + 1.25

-3.5x = -0.75

3.5x = 0.75

x = [tex]\frac{0.75}{3.5}[/tex]

9) x(x-4)+5 = 10x - 20 + x²

x*x + x*(-4) + 5 = 10x - 20 + x²

x² - 4x + 5 = 10x - 20 + x²

-4x - 10x = -20 - 5

-14x = -25

14x = 25

x = [tex]\frac{25}{14}[/tex]