45. Раскойте скобки и приведите подобные слагаемые:

Решение:

1. A) \( 2(4x+1)+4(2x+6) = 8x + 2 + 8x + 24 = 16x + 26 \)
2. Б) \( 7(x+2y)+6(y-x) = 7x + 14y + 6y - 6x = x + 20y \)
3. B) \( 8(x+y+8)+5(x-4y-15) = 8x + 8y + 64 + 5x - 20y - 75 = 13x - 12y - 11 \)
4. Г) \( 2,1(2x−y)+4,2(x+3y)+1,2(x-4y) = 4,2x - 2,1y + 4,2x + 12,6y + 1,2x - 4,8y = (4,2+4,2+1,2)x + (-2,1+12,6-4,8)y = 9,6x + 5,7y \)
5. Д) \( 2(a+2b-3c+4)+3(2a-3b+5c+6) = 2a + 4b - 6c + 8 + 6a - 9b + 15c + 18 = (2+6)a + (4-9)b + (-6+15)c + (8+18) = 8a - 5b + 9c + 26 \)
6. E) \( 3(5x+7)+2(3x+5) = 15x + 21 + 6x + 10 = 21x + 31 \)
7. Ë) \( 5(x−y)+4(3x+2y) = 5x - 5y + 12x + 8y = 17x + 3y \)
8. Ж) \( 7(x-2y+10)+6(3y-4x-1) = 7x - 14y + 70 + 18y - 24x - 6 = (7-24)x + (-14+18)y + (70-6) = -17x + 4y + 64 \)
9. 3) \( 3,4(2x-y)+2,3(x+3y)+1,1(5x-7y) = 6,8x - 3,4y + 2,3x + 6,9y + 5,5x - 7,7y = (6,8+2,3+5,5)x + (-3,4+6,9-7,7)y = 14,6x - 4,2y \)
10. И) \( 3(5a-2b+7c-11)+4(a+3b-6c+8) = 15a - 6b + 21c - 33 + 4a + 12b - 24c + 32 = (15+4)a + (-6+12)b + (21-24)c + (-33+32) = 19a + 6b - 3c - 1 \)
11. Й) \( 7(2х-6)+4(3+7x) = 14x - 42 + 12 + 28x = (14+28)x + (-42+12) = 42x - 30 \)
12. K) \( 2,5(x+3)+2(1-5x) = 2,5x + 7,5 + 2 - 10x = (2,5-10)x + (7,5+2) = -7,5x + 9,5 \)
13. Л) \( 2\frac{1}{7}(3,5a+7b-14)+4(2a-b+5) = \frac{15}{7}(\frac{7}{2}a+7b-14)+8a-4b+20 = \frac{15}{7}\frac{7}{2}a + \frac{15}{7}7b - \frac{15}{7}14 + 8a-4b+20 = \frac{15}{2}a + 15b - 30 + 8a - 4b + 20 = 7,5a + 15b - 30 + 8a - 4b + 20 = (7,5+8)a + (15-4)b + (-30+20) = 15,5a + 11b - 10 \)
14. M) \( 5(3x-2y+6)+8(2x-3y-9) = 15x - 10y + 30 + 16x - 24y - 72 = (15+16)x + (-10-24)y + (30-72) = 31x - 34y - 42 \)
15. H) \( 3(x-y)+4(2x-7)+8(3y+5) = 3x - 3y + 8x - 28 + 24y + 40 = (3+8)x + (-3+24)y + (-28+40) = 11x + 21y + 12 \)