13. Вынесение обшего множителя за скобки. B A m²n³ + mn4 - m³n5 C № ab + ac 5a4b - 10a3b² + 15a3b x(y - 7) + a(y - 7) Ng 1 mn - pm 2x5y6 - 3x4y5 +x6y7 b(k + 5)-n(5+k) 2 - xy + χα 3a(x - y) +2b(x - y) y(p-6)+b(6-p) 3 - pk - mk (c + 2) + 4a(c + 2) p(t-8) - k(8-t) 4 6x+6y 8(m+n)²-4(m+n) 5(a - b)²-3(α-b) 5 3m-3n 7(a - b)²-6(b-α) 4(a – 2b)² - (2b - α) 6 4α - 12b p(2+α) - 3(a+2) 4ab + 6ac x(a - b)² +y(b − a)² 7 -15x - 25y k(x + y)²-p(y+x) 5(x - y)² - 10(x - y)³ 8 7x - y)²-(x - y)² 48c + 36q a(x - y) + b(y-x) 4x(x+y) - 5x2(x+y) 9 10 13α - 13 (x - y)²-p(y-x) 9y³(p-2) -3y²(p-2) 11 4x³ + 2 a(p-k)+b(k-p)² 3x²(1-y) - 6x³(y-1) 12 - 10 - 5α 4(a – 2b)² - (2b - α) α²(7- b) + a(b - 7) 13 4ab + 6ac x(a - b)² +y(b − a)² t³(3 - x) - t²(x - 3) 14 2a - 8ab x(a - b)² - y(b-a)3 q²(1 - x) +q³(x - 1) 15 7y2 - 49y 5(x - y)² - 10(x - y) 5x³y - 10x2y2 - 15xy 16 - 5x3 + 15x2 5(x - y) - 10(x - y)² 8α4 - 12α³ +16α5 17 a²b4-ab³ 8x(a - b) - 4x²(a - b) 6x2y-15xy² -3xy³ 18 a²b+a6b 6x²(a - b) + 9x(a - b) 24x5y6 - 16x2y7 19 12m²n + 6m² (x - y)² + 2x (x - y) 16a3b5 + 32a3b4 20 14x²y -7x3 (x - y)²+ (x - y) 8n512n7 + 16n4

Решение заданий на вынесение общего множителя за скобки.

1. ab + ac = a(b + c)

2. mn - pm = m(n - p)

3. - xy + xα = x(-y + α)

4. 6x + 6y = 6(x + y)

5. 3m - 3n = 3(m - n)

6. 4α - 12b = 4(α - 3b)

7. -15x - 25y = -5(3x + 5y)

8. 48c + 36q = 12(4c + 3q)

9. 13α - 13 = 13(α - 1)

10. 4x³ + 2 = 2(2x³ + 1)

11. - 10 - 5α = -5(2 + α)

12. 4ab + 6ac = 2a(2b + 3c)

13. 2a - 8ab = 2a(1 - 4b)

14. 7y² - 49y = 7y(y - 7)

15. - 5x3 + 15x2 = -5x²(x - 3)

16. a²b4-ab³ = ab³(ab - 1)

17. 12m²n + 6m² = 6m²(2n + 1)

18. 14x²y -7x3 = 7x²(2y - x)

19. 5a⁴b - 10a³b² + 15a³b = 5a³b(a - 2b + 3)

20. 2x⁵y⁶ - 3x⁴y⁵ + x⁶y⁷ = x⁴y⁵(2xy - 3 + x²y²)

21. 3a(x - y) + 2b(x - y) = (x - y)(3a + 2b)

22. (c + 2) + 4a(c + 2) = (c + 2)(1 + 4a)

23. 8(m+n)² - 4(m+n) = 4(m + n)(2(m + n) - 1)

24. p(2 + α) - 3(a + 2) = (2 + α)(p - 3)

25. 4(a – b) + 3(b – a)² = (a - b)(4 - 3(b - a))

26. k(x + y)² - p(y + x) = (x + y)(k(x + y) - p)

27. a(x - y) + b(y - x) = (x - y)(a - b)

28. 4x(x+y) - 5x²(x+y) = (x + y)(4x - 5x²)

29. 9y³(p-2) - 3y²(p-2) = 3y²(p - 2)(3y - 1)

30. 3x²(1-y) - 6x³(y-1) = 3x²(1 - y)(1 + 2x)

31. α²(7- b) + a(b - 7) = a(7 - b)(α - 1)

32. t³(3 - x) - t²(x - 3) = t²(3 - x)(t - 1)

33. x(a - b)² +y(b – a)² = (a - b)²(x + y)

34. q²(1 - x) + q³(x - 1) = q²(1 - x)(1 + q)

35. 5x³y - 10x²y² - 15xy = 5xy(x² - 2xy - 3)

36. 8α⁴ - 12α³ + 16α⁵ = 4α³(2α - 3 + 4α²)

37. 6x²y - 15xy² - 3xy³ = 3xy(2x - 5y - y²)

38. 16a³b⁵ + 32a³b⁴ = 16a³b⁴(b + 2)

39. (x - y)² + 2x (x - y) = (x - y)(x - y + 2x)

40. 8n⁵ - 12n⁷ + 16n⁴ = 4n⁴(2n - 3n³ + 4)

Ответ: смотри решение выше