Which of the following correctly demonstrates the use of the Commutative Property of Multiplication? (1 point))

2(b ^ 10 + z ^ 11) = (b ^ 10 + z ^ 11) ยท

3(b ^ 10 + 4) = 3(4 + b ^ 10) * 3

O 11(b + z) = 11b + 11z

z ^ 11 * 2 = z ^ 11 + 2

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 months ago

The Commutative Property of Multiplication states that changing the order of the factors does not change the product. In other words, \( a \times b = b \times a \).

Let's analyze each option:

1. **\( 2(b^{10} + z^{11}) = (b^{10} + z^{11}) \cdot 2 \)** - This shows the associative property of multiplication instead of commuting (though the multiplication is commuted).

2. **\( 3(b^{10} + 4) = 3(4 + b^{10}) \)** - This demonstrates the rearrangement of terms in a sum, not multiplication. It does not illustrate the Commutative Property of Multiplication.

3. **\( 11(b + z) = 11b + 11z \)** - This option illustrates the Distributive Property, which relates to multiplication distributed over addition but does not demonstrate the Commutative Property.

4. **\( z^{11} \cdot 2 = z^{11} + 2 \)** - This equation is incorrect as it shows an addition instead of multiplication.

Based on these evaluations, none of the options provided correctly demonstrates the Commutative Property of Multiplication. If forced to choose the closest one regarding multiplication, the first option does acknowledge the commutative nature of multiplication, depending on interpretation, but ultimately is focused on associative properties.