Question

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

5(p+b)=5p+5b


4(h^12+7)=4(7+h^12)


3(x^12=y^4)=(x^12=y^4)⋅3

w^3⋅8=w^3+8

Answer 1

3(x^6+y^4)=(x^6+y^4)*3 is incorrectly formatted? It the only answer close to being Commutative Property of Multiplication.

Answer 2

The Commutative Property of Multiplication states that the order of factors can be changed without affecting the product. In other words, for any numbers \(a\) and \(b\), \(a \times b = b \times a\).

Looking at the options provided:

1. \(5(p+b) = 5p + 5b\) - This demonstrates the Distributive Property, not the Commutative Property.

2. \(4(h^{12} + 7) = 4(7 + h^{12})\) - This also demonstrates the Distributive Property, as well as the Commutative Property of Addition but not specifically of Multiplication.

3. \(3(x^{12} = y^{4}) = (x^{12} = y^{4}) \cdot 3\) - This does not correctly demonstrate the Commutative Property and looks incorrectly formatted.

4. \(w^3 \cdot 8 = w^3 + 8\) - This is incorrect; it doesn’t demonstrate any property correctly.

None of the given options correctly illustrate the Commutative Property of Multiplication. An example would be something like \(3 \cdot 4 = 4 \cdot 3\).

Answer 3

You're absolutely correct, and I apologize for the oversight. The expression \(3(x^6 + y^4) = (x^6 + y^4) \cdot 3\) does indeed illustrate the Commutative Property of Multiplication, as it shows that multiplying the sum \(x^6 + y^4\) by \(3\) can be done in either order.

So to clarify:

The correct answer that demonstrates the Commutative Property of Multiplication is:

**3(x^6 + y^4) = (x^6 + y^4) * 3**

Thank you for your patience, and I appreciate your understanding!