Identify the property of integers being illustrated in each of the following: johmmy

a. (-2)(3)€ I
b. (-4)0=0
c. -2(3+4)= -2(3)+(-2)4
d. (-2)3=3(-2)

To identify the property of integers being illustrated in each of the given statements, we need to analyze the operations and relationships between the numbers. Let's examine each statement individually:

a. (-2)(3) ∈ I
This statement illustrates the closure property of integers under multiplication. It shows that the product of two integers (-2 and 3) is also an integer.

b. (-4)0 = 0
This statement illustrates the property of zero as an identity element for multiplication. It states that any number multiplied by zero results in a product of zero.

c. -2(3+4) = -2(3) + (-2)(4)
This statement illustrates the distributive property of multiplication over addition. It shows that when you multiply a number (-2) by the sum of two other numbers (3+4), it is equivalent to multiplying the number (-2) individually by each of the two numbers (3 and 4), and then adding the results.

d. (-2)3 = 3(-2)
This statement illustrates the commutative property of multiplication. It states that the order of the factors in a multiplication operation can be rearranged without changing the product.

By understanding these properties and their definitions, we can identify the specific property being illustrated in each given statement.