Упростите выражение: (n+1) (2n-3) + (n-1) (3n+1) (x-y) (2x-3y) - (3x-y) (2x+y) (2a+3) (2a+3) - (2a+1) (2a-1) (3c-d) (d+3c) + (4c-d) (c-4d)

Раскроем скобки и упростим выражения:

1) (n + 1) * (2n - 3) + (n - 1) * (3n + 1) = 2n^2 - 3n + 2n - 3 + 3n^2 + n - 3n - 1 = 5n^2 - 3n - 4;

2n^2 + 3n^2 = 5n^2;

-3n + 2n + n - 3n = - 3n;

-3 - 1 = - 4.

2) (x - y) * (2x - 3y) - (3x - y) * (2x + y) = 2x^2 - 3xy - 2xy - 6x^2 - 3xy + 2xy + y^2 = - 4x^2 - 6xy + y^2;

3) (2a + 3) * (2a + 3) - (2a + 1) * (2a - 1) = 4a^2 + 12a + 9 - 4a^2 + 1 = 12a + 10;

4) (3c - d) * (d + 3c) + (4c - d) * (c - 4d) = (3c - d) * (3c + d) + (4c - d) * (c - 4d) = 9c^2 - d^2 + 4c^2 - 16cd - cd + 4d^2 = 13c^2 + 3d^2 - 17cd.