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

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

1 answer

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})