Which of the following correctly demonstrates the use of the commutative property of multiplication

The commutative property of multiplication states that the order in which two numbers are multiplied does not change the product. In mathematical terms, this can be stated as \( a \times b = b \times a \).

Looking at your expression, \( 3(b \cdot 10 + 4) = 3(4 + b \cdot 10) \), the use of the commutative property is present in the rearrangement of terms within the parentheses.

For the left-hand side:
- \( b \cdot 10 + 4 \)

For the right-hand side:
- \( 4 + b \cdot 10 \)

In both cases, the multiplication of \( b \) and \( 10 \) remains unchanged, but the addition operation demonstrates the rearrangement of the terms according to the commutative property of addition, not multiplication.

The correct demonstration of the commutative property of multiplication would solely involve rearranging the multiplication factors. For example, \( a \cdot b = b \cdot a \), such as \( 3 \cdot (b \cdot 10) = 3 \cdot (10 \cdot b) \).

Therefore, just to clarify, the equation you gave shows an application of the commutative property of addition rather than multiplication. The use of the commutative property of multiplication would need to show that the order of multiplication factors can be switched without affecting the outcome.