Question

Which of the following correctly demonstrates the use of the Commutative Property of Multiplication?
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

z11⋅2=z11+2
z superscript 11 baseline times 2 equals z superscript 11 baseline plus 2

3(b10+4)=3(4+b10)3

Answer 1

The Commutative Property of Multiplication states that changing the order of the factors does not change the product. In other words, for any numbers \( a \) and \( b \), the property can be stated as:

\[ a \cdot b = b \cdot a \]

Now, let's look at the provided options:

1. **11(b + z) = 11b + 11z**: This demonstrates the Distributive Property, not the Commutative Property.

2. **2(b^{10} + z^{11}) = (b^{10} + z^{11}) \cdot 2**: This illustrates the Commutative Property, since it shows that multiplying the expression by 2 can occur on either side.

3. **z^{11} ⋅ 2 = z^{11} + 2**: This is incorrect. This statement does not apply the Commutative Property correctly; multiplication is not addition.

4. **3(b^{10} + 4) = 3(4 + b^{10})**: This correctly demonstrates the Commutative Property of Addition in the context of the terms in parentheses; however, it doesn't focus solely on multiplication.

The only response that correctly demonstrates the use of the Commutative Property of Multiplication is:

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