(2x-1)(4x²+2x+1)-8x(x²+1)=3x+4 (x+2)³-x²(x+5)-(x+1)(x-1)= 0 x³+y²+2xy(x+y) (3a-0,6)³ 27c³-125 8x³+12x²y+6xy²+y³ x³+8

Решим уравнения:

1) (2 * x - 1) * (4 * x² + 2 * x + 1) - 8 * x * (x² + 1) = 3 * x + 4;   

8 * x³ - 1 - 8 * x³  - 8 * x = 3 * x + 4; 

-1 - 8 * x = 3 * x + 4; 

-8 * x - 3 * x = 4 + 1; 

-8 * x - 3 * x = 5; 

-11 * x = 5; 

x = -5/11. 

2) (x + 2)³ - x² * (x + 5) - (x + 1) * (x - 1) = 0;  

x³ + 4 * x² + 8 * x + 8 - x³ - 5 * x² - x² + 1 = 0; 

-2 * x² + 8 * x + 9 = 0;  

x1 =  2 + 0.5√34; 

x2 =  2 - 0.5√34. 

Упростим выражения:

3) x³ + y³ + 2 * x * y * (x + y) =  (x + y) * (x² + x * y + y²); 

4) (3 * a - 0,6)³ = (3 * a - 0.6) * (9 * a² + 3.6 * a + 0.36); 

5) 27  * c³ - 125 = (3 * c)³ - 5³ = (3 * c - 5) * (9 * c² + 15 * c + 25); 

6) 8 * x³ + 12 * x² * y + 6 * x * y² + y³ = (2 * x + y)³; 

7) x³ + 8 = (x + 2) * (x² - 2 * x + 4); 

8) (a + 2) * (a² - 2 * a + 4) - 8 = a³ + 8 - 8 = a³; 

9) (a - b)³ - a³ = (a - b - a) * ((a - b)² + a * (a - b) + a²) = -b * (a² - 2 * a * b + b² + a² - a * b + a²) = -b * (3 * a² - 3 * a * b + b²).