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]
