Let's solve the factorization problems shown in the image one by one:

31. $5a + 5b = 5( \square + \square )$ $5a + 5b = 5(a + b)$

32. $3g + 9m = 3( \square + \square )$ $3g + 9m = 3(g + 3m)$

33. $2a - 4 = 2( \square - \square )$ $2a - 4 = 2(a - 2)$

34. $5r + 10 = 5( \square + \square )$ $5r + 10 = 5(r + 2)$

35. $7b - 14 = 7( \square - \square )$ $7b - 14 = 7(b - 2)$

36. $4ab + 8b = 4b( \square + \square )$ $4ab + 8b = 4b(a + 2)$

37. $3xy - 9x = 3x( \square - \square )$ $3xy - 9x = 3x(y - 3)$

38. $5pq + 10p = 5p( \square + \square )$ $5pq + 10p = 5p(q + 2)$

39. $13p - ap = p( \square - \square )$ $13p - ap = p(13 - a)$

40. $17c + ac = c( \square + \square )$ $17c + ac = c(17 + a)$

Would you like any further explanation on any of these steps?

Here are some related questions to deepen your understanding:

1. How do you identify the common factor in an expression before factoring?
2. Why is factoring important in solving algebraic equations?
3. How can you factor quadratic expressions using a similar method?
4. What happens when there is no common factor between terms?
5. How would you factor a trinomial like $x^2 + 5x + 6$?

Tip: When factoring, always start by identifying the greatest common factor (GCF) before breaking the expression down further.