Решите задания на раскрытие скобок и упрощение выражений с 17 по 39.

Для раскрытия скобок воспользуемся правилами: если перед скобками стоит знак «+», скобки убираем, сохраняя знаки слагаемых; если «−», знаки всех слагаемых внутри скобок меняем на противоположные. Раскрытие начинаем с внутренних скобок. 17) $a+[b-(c-d)] = a+b-c+d$ 18) $a-[b+(c-d)] = a-b-c+d$ 19) $a-[(b-c)-d] = a-b+c+d$ 20) $a-[(b-c)+d] = a-b+c-d$ 21) $3x-[5x-(2x-3)] = 3x-[5x-2x+3] = 3x-5x+2x-3 = -3$ 22) $(4n-2)-[(n-4)-10] = 4n-2-n+4+10 = 3n+12$ 23) $12a-[(5a-7)-(4+3a)] = 12a-[5a-7-4-3a] = 12a-5a+7+4+3a = 10a+11$ 24) $5b-[2c-(3b-8c)]+4c = 5b-[2c-3b+8c]+4c = 5b-2c+3b-8c+4c = 8b-6c$ 25) $5a^2-3b^2+[-(a^2-2ab-b^2)+(5a^2-2ab+3b^2)]-(3a^2-4b^2) = 5a^2-3b^2-a^2+2ab+b^2+5a^2-2ab+3b^2-3a^2+4b^2 = 6a^2+5b^2$ 26) $(-2xy+y^2)+[x^2-(3y^2+2x^2-4xy)+5y^2]-(3xy-4x^2) = -2xy+y^2+x^2-3y^2-2x^2+4xy+5y^2-3xy+4x^2 = 3x^2+3y^2-xy$ 27) $[-5m^2+2n^2+(3m-4n^2)-2m]+6n^2-[3n^2-7m^2+(-2n^2+2m)]-(4m-6m^2) = -5m^2+2n^2+3m-4n^2-2m+6n^2-3n^2+7m^2+2n^2-2m-4m+6m^2 = 8m^2+3n^2-5m$ 28) $3a^{n+1}-[2b^n-(a^n-5b^n+2a^{n+1})+b^n-4a^{n+1}]-(5a^{n+1}-3a^n-7b^n) = 3a^{n+1}-2b^n+a^n-5b^n+2a^{n+1}-b^n+4a^{n+1}-5a^{n+1}+3a^n+7b^n = 4a^{n+1}+4a^n$ 29) $a - {b - [c - (d - m)] - (d - c)} = a - b + c - d + m + d - c = a - b + m$ 30) $a - {b + [c - (d + m)] - (b - a)} = a - b - c + d + m + b - a = d + m$ 31) $a + {b - [c + (d - m)] - c} = a + b - c - d + m - c = a + b - 2c - d + m$ 32) $a + {b - [(d - c) + m] + d} = a + b - d + c - m + d = a + b + c - m$ 33) $2m - {3m - [4m - (5m + 6m)] - 2m} = 2m - {3m - [4m - 11m] - 2m} = 2m - {3m + 7m - 2m} = 2m - 8m = -6m$ 34) $8x - {5x + [7x - (10x - 2x)] - 3x} = 8x - {5x + [7x - 8x] - 3x} = 8x - {5x - x - 3x} = 8x - x = 7x$ 35) $3a - {2c - [6a - (c - b) + 3c + (a + 8b - 4c)] - 4b} - [5a - (3c - 7b)] = 3a - {2c - [6a - c + b + 3c + a + 8b - 4c] - 4b} - 5a + 3c - 7b = 3a - {2c - [7a + 9b - 2c] - 4b} - 5a + 3c - 7b = 3a - {2c - 7a - 9b + 2c - 4b} - 5a + 3c - 7b = 3a - 4c + 7a + 13b - 5a + 3c - 7b = 5a + 6b - c$ 36) $a + [-4c + (-2b + a)] - {5b + [3c - 2a - (a + b)] + 4a - (b + 5c)} = a - 4c - 2b + a - {5b + [3c - 2a - a - b] + 4a - b - 5c} = 2a - 2b - 4c - {5b + 3c - 3a - b + 4a - b - 5c} = 2a - 2b - 4c - {3b - 2c + a} = 2a - 2b - 4c - 3b + 2c - a = a - 5b - 2c$ 37) {3z - [(2x - y)] + 2x - {4y - [x - (3z - 4y) + 2z + (x - 3y - 5z)] - (6y - 4z)}} = 3z - 2x + y + 2x - {4y - [x - 3z + 4y + 2z + x - 3y - 5z] - 6y + 4z} = y + 3z - {4y - [2x + y - 6z] - 6y + 4z} = y + 3z - {4y - 2x - y + 6z - 6y + 4z} = y + 3z - {-3y - 2x + 10z} = y + 3z + 3y + 2x - 10z = 2x + 4y - 7z 38) $x - {2y + [3z - (x + z) - 7x] - (2z - 4x)} - [2x - (3y - 5z)] + [-6x - (-y - 4z)] = x - {2y + [3z - x - z - 7x] - 2z + 4x} - 2x + 3y - 5z - 6x + y + 4z = x - {2y - 8x + 2z - 2z + 4x} - 8x + 4y - z = x - {2y - 4x} - 8x + 4y - z = x - 2y + 4x - 8x + 4y - z = -3x + 2y - z$ 39) $(3m + 5n) - {9m - [6m + 2n - (12n - 10m)] - m - (7m - 4n)} = 3m + 5n - {9m - [6m + 2n - 12n + 10m] - m - 7m + 4n} = 3m + 5n - {9m - [16m - 10n] - 8m + 4n} = 3m + 5n - {m - 16m + 10n + 4n} = 3m + 5n - {-15m + 14n} = 3m + 5n + 15m - 14n = 18m - 9n$