Let's analyze the properties illustrated by the equations provided in the image:

a. $(a + b) + c = a + (b + c)$
This represents the Associative Property of Addition. It shows that when adding three numbers, the grouping (or association) of the numbers doesn't affect the sum.

b. $a(bc) = (ab)c$
This is an example of the Associative Property of Multiplication. It states that the way in which numbers are grouped when multiplying doesn't change the result.

c. $a(b + c) = ab + ac$
This illustrates the Distributive Property. It shows that multiplying a number by a sum is the same as multiplying the number by each addend individually and then adding the results.

Let me know if you'd like further details or have any questions!

Here are 5 related questions to expand your understanding:

1. What is the difference between the commutative and associative properties?
2. Can you provide an example of the commutative property of multiplication?
3. How would the distributive property apply to subtraction instead of addition?
4. Can you apply the associative property to more than three terms in addition or multiplication?
5. What is the practical use of the distributive property in solving equations?

Tip: The distributive property is especially useful when simplifying algebraic expressions and solving equations involving parentheses.