5. (2x+y)³ + (y-x)³
=> 8x³ + 12x²y + 6xy² + y³ + y³ - 3yx² + 3x²y - x³
=> 7x³ + 15x²y + 6xy² + 2y³

6. 2(y-x)³ - (2x-y)³
=> 2(y³ - 3yx² + 3x²y - x³) - (8x³ - 12x²y + 6xy² - y³)
=> -16x³ + 24x²y - 12xy² + 2y³

7. (2x+y)³ - (x-2y)³
=> 8x³ + 12x²y + 6xy² + y³ - (x³ - 3x²(2y) + 3x(2y)² - (2y)³)
=> 8x³ + 12x²y + 6xy² + y³ - (x³ - 6x²y + 12xy² - 8y³)
=> 7x³ + 18x²y - 6xy² + y³ + 8y³
=> 7x³ + 18x²y - 6xy² + 9y³

8. (2x-3)³ - 2x(2x+1)²
=> 8x³ - 36x² + 54x - 27 - 8x³ - 8x²
=> -44x² + 54x - 27

9. (3x-1)³ - 27x²(x-1)
=> 27x³ - 27x² + 9x - 1 - 27x³ + 27x²
=> 9x - 1

10. (2x+1)³ - 8x(x-1)²
=> 8x³ + 12x² + 6x + 1 - 8x³ + 16x² - 16x
=> 28x² - 10x + 1

11. (x+1)³ - (x-4)(x+4) + x³
=> x³ + 3x² + 3x + 1 - x² - 16 + x³
=> 2x³ + 2x² + 3x - 15

12. (x+2)³ - x(x+3)(x-3)
=> x³ + 6x² + 12x + 8 - x³
=> 6x² + 12x + 8

13. (x-2)³ - x(x-2)(x+2) + 6x(x-3)
=> x³ - 6x² + 12x - 8 - x³ + 6x(x-3)
=> -12x² + 30x - 8

14. x(x-5)(x+5) - (x-5) + 100x
=> x³ - 5x² - 5x² + 25x - x + 5 + 100x
=> x³ - 10x² + 126x + 5