Задание 13. Приведите подобные слагаемые.

Решение:

Для приведения подобных слагаемых нужно сложить их коэффициенты и результат умножить на общую буквенную часть.

Колонка А:

1. \( 2a + 11a - 13a = (2 + 11 - 13)a = 0a = 0 \)
2. \( 6b + b + 2b = (6 + 1 + 2)b = 9b \)
3. \( 2m + 3m + 5m + m = (2 + 3 + 5 + 1)m = 11m \)
4. \( e + e + e = (1 + 1 + 1)e = 3e \)
5. \( 43k + 12k = (43 + 12)k = 55k \)
6. \( 3s + 6s + s + 11s = (3 + 6 + 1 + 11)s = 21s \)
7. \( 5y - 3y + 6y - y = (5 - 3 + 6 - 1)y = 7y \)
8. \( 25p - 19p - 3p = (25 - 19 - 3)p = 3p \)
9. \( 14n - 8n - 3n + n = (14 - 8 - 3 + 1)n = 4n \)
10. \( 3h + 18h - 14h + 5h = (3 + 18 - 14 + 5)h = 12h \)
11. \( s + 5s + s - 7s = (1 + 5 + 1 - 7)s = 0s = 0 \)
12. \( 32a - 18a + 15a = (32 - 18 + 15)a = 29a \)
13. \( 4k + 22k - 19k = (4 + 22 - 19)k = 7k \)
14. \( z + 3z - 2z + 89z = (1 + 3 - 2 + 89)z = 91z \)
15. \( 12e - 5e + 3e - e = (12 - 5 + 3 - 1)e = 9e \)

Колонка Б:

1. \( 2c + d + bc + d + 2c + bc + 7c = (2 + 2 + 7)c + (d + d) + (bc + bc) = 11c + 2d + 2bc \)
2. \( a + 2q + 2a + 4q = (a + 2a) + (2q + 4q) = 3a + 6q \)
3. \( 6s + 2h + 2s + 3 = (6s + 2s) + 2h + 3 = 8s + 2h + 3 \)
4. \( 5u + 4 + 6 + 2u = (5u + 2u) + (4 + 6) = 7u + 10 \)
5. \( 3f + 2g + 2 + f + g = (3f + f) + (2g + g) + 2 = 4f + 3g + 2 \)
6. \( 23w - 5w - 6 - p = (23w - 5w) - 6 - p = 18w - 6 - p \)
7. \( 5 + x - 6 + 1 - x = (x - x) + (5 - 6 + 1) = 0 + 0 = 0 \)
8. \( 18n + 12m - 5n - 1 = (18n - 5n) + 12m - 1 = 13n + 12m - 1 \)
9. \( 2x - 5y + z - 4x + 3z - y = (2x - 4x) + (-5y - y) + (z + 3z) = -2x - 6y + 4z \)
10. \( 6v - 9m - 13v + 5 - 2v = (6v - 13v - 2v) - 9m + 5 = -9v - 9m + 5 \)
11. \( -c - c - c = (-1 - 1 - 1)c = -3c \)
12. \( -x - 2x + 5x = (-1 - 2 + 5)x = 2x \)
13. \( 90s - 64s + 45 + 36 = (90s - 64s) + (45 + 36) = 26s + 81 \)
14. \( 27v + 60y - 15y - 90v = (27v - 90v) + (60y - 15y) = -63v + 45y \)
15. \( 20h + k - 20k - h - h = (20h - h - h) + (k - 20k) = 18h - 19k \)

Колонка В:

1. \( a + 3h + 5h - 6a - a + 6a + 3h - 5h - 5a - 8h = (a - 6a - a + 6a - 5a) + (3h + 5h - 5h - 8h) = -5a - 5h \)
2. \( 3s - 8d - 12s + 5d = (3s - 12s) + (-8d + 5d) = -9s - 3d \)
3. \( -f - 11y - 3y + 7f = (-f + 7f) + (-11y - 3y) = 6f - 14y \)
4. \( 3q - 5n - 11q + 2 + 8n = (3q - 11q) + (-5n + 8n) + 2 = -8q + 3n + 2 \)
5. \( -4 + 7c - 12 - 9c = (7c - 9c) + (-4 - 12) = -2c - 16 \)
6. \( -2z + 5s - 3s + 2z - 2s = (-2z + 2z) + (5s - 3s - 2s) = 0 + 0 = 0 \)
7. \( -36n - 8u + 12n + 9u = (-36n + 12n) + (-8u + 9u) = -24n + u \)
8. \( a - b - a - b - a - b = (a - a - a) + (-b - b - b) = -2a - 3b \)
9. \( 3a - 4h + 6a - 4 - 8a = (3a + 6a - 8a) - 4h - 4 = a - 4h - 4 \)
10. \( 15d + k - 13 - d + 2 = (15d - d) + k - (13 - 2) = 14d + k - 11 \)
11. \( -3 + 15r - 19 - 20r = (15r - 20r) + (-3 - 19) = -5r - 22 \)
12. \( 19n - 51n + 12n - 33 = (19n - 51n + 12n) - 33 = -20n - 33 \)
13. \( -m - 3m + 2m = (-1 - 3 + 2)m = -2m \)
14. \( -t - 4t + 3t = (-1 - 4 + 3)t = -2t \)
15. \( -u - 8u + 10u = (-1 - 8 + 10)u = u \)

Ответ: Результаты приведены в таблице выше.