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

Question

Responses

11(b+z)=11b+11z
11 left parenthesis b plus z right parenthesis equals 11 b plus 11 z

2(b10+z11)=(b10+z11)⋅2
2 left parenthesis b superscript 10 baseline plus z superscript 11 baseline right parenthesis equals left parenthesis b superscript 10 baseline plus z superscript 11 baseline right parenthesis times 2

3(b10+4)=3(4+b10)3
3 left parenthesis b superscript 10 baseline plus 4 right parenthesis equals 3 left parenthesis 4 plus b superscript 10 baseline right parenthesis 3

z11⋅2=z11+2

Answer 1

The Commutative Property of Multiplication states that the order in which two numbers are multiplied does not change the product. In other words, $a\times b=b\times a$.

Let's analyze each option:

1. $11(b+z)=11b+11z$ - This represents the Distributive Property, not the Commutative Property.

2. $2(b^{10}+z^{11})=(b^{10}+z^{11})\cdot 2$ - This also illustrates the Commutative Property as it shows that multiplying by $2$ can be done in either order.

3. $3(b^{10}+4)=3(4+b^{10})$ - This is a correct use of the Commutative Property as well, since it shows that the expression inside the parentheses can be rearranged.

4. $z^{11}\cdot 2=z^{11}+2$ - This is incorrect as the operations are not correctly illustrated.

Therefore, the options that demonstrate the use of the Commutative Property of Multiplication are options 2 and 3. However, specifically for identifying the "use" of the Commutative Property prominently, option 3 is the clearest demonstration of the property.

Final answer: 3(b^{10}+4) = 3(4+b^{10})