Distributive, Associative, or neither?
3(bz)=(3b)z
To determine whether the given expression, 3(bz), is distributive, associative, or neither, we need to understand the properties of these operations.
1. Distributive property:
The distributive property states that for any real numbers a, b, and c:
a(b + c) = ab + ac
2. Associative property:
The associative property states that for any real numbers a, b, and c:
(a + b) + c = a + (b + c)
Now, let's apply these properties to the expression 3(bz) and (3b)z:
Expression 1: 3(bz)
We can apply the distributive property to this expression by multiplying the 3 outside the parentheses with bz inside:
3(bz) = 3 * b * z
Expression 2: (3b)z
Similarly, we can distribute the 3 inside the parentheses to the b:
(3b)z = 3 * b * z
By comparing both expressions, we can see that they are equal:
3(bz) = (3b)z
This illustrates the distributive property, as the multiplication is distributed over the addition inside the parentheses. Therefore, the given expression, 3(bz)=(3b)z, is an example of the distributive property.