302 Упростите выражение: a) 2(a + b) + 3(a + b) + 2a; б) 5(x - 2) - 2(x + z); в) 2(2r - 3s) - 3(r - 2s); г) 6(2a + c) + 2(6a - c) - 4c; д) 3(x - 1) + (x - 2) - x; e) 5n - 3(n + 2) + (n - 6); ж) m - (2m - 6) + 3(m - 3); 3) 2(3x + 1) - (x-2) - 3x.

Решение:

1. а) \( 2(a + b) + 3(a + b) + 2a = 2a + 2b + 3a + 3b + 2a = (2a + 3a + 2a) + (2b + 3b) = 7a + 5b \)
2. б) \( 5(x - 2) - 2(x + z) = 5x - 10 - 2x - 2z = (5x - 2x) - 2z - 10 = 3x - 2z - 10 \)
3. в) \( 2(2r - 3s) - 3(r - 2s) = 4r - 6s - 3r + 6s = (4r - 3r) + (-6s + 6s) = r \)
4. г) \( 6(2a + c) + 2(6a - c) - 4c = 12a + 6c + 12a - 2c - 4c = (12a + 12a) + (6c - 2c - 4c) = 24a \)
5. д) \( 3(x - 1) + (x - 2) - x = 3x - 3 + x - 2 - x = (3x + x - x) + (-3 - 2) = 3x - 5 \)
6. е) \( 5n - 3(n + 2) + (n - 6) = 5n - 3n - 6 + n - 6 = (5n - 3n + n) + (-6 - 6) = 3n - 12 \)
7. ж) \( m - (2m - 6) + 3(m - 3) = m - 2m + 6 + 3m - 9 = (m - 2m + 3m) + (6 - 9) = 2m - 3 \)
8. з) \( 2(3x + 1) - (x - 2) - 3x = 6x + 2 - x + 2 - 3x = (6x - x - 3x) + (2 + 2) = 2x + 4 \)

Ответ: а) 7a + 5b; б) 3x - 2z - 10; в) r; г) 24a; д) 3x - 5; е) 3n - 12; ж) 2m - 3; з) 2x + 4.