Which of the following correctly demonstrates the use of the Commutative PropertWy 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 changing the order of the factors does not change the product. In other words, \( a \times b = b \times a \).

Looking at the responses provided:

  1. \( 11(b + z) = 11b + 11z \) demonstrates the Distributive Property, not the Commutative Property.
  2. \( 2(b^{10}+z^{11}) = (b^{10}+z^{11}) \cdot 2 \) demonstrates the commutative property by showing that the order of multiplication can be swapped, so this one is correct.
  3. \( 3(b^{10} + 4) = 3(4 + b^{10}) \) also demonstrates the Commutative Property of addition within the parentheses but represents multiplication outside the parentheses. This is indeed an example of the Commutative Property for addition in the context but it doesn't purely demonstrate multiplication alone.
  4. \( 3z^{11} \cdot 2 = z^{11} + 2 \) is incorrect as it incorrectly describes an equality that does not hold true in both sides.

Given these explanations, the response that correctly demonstrates the use of the Commutative Property of Multiplication is:

2. \( 2(b^{10}+z^{11}) = (b^{10}+z^{11}) \cdot 2 \)