Which expressions correctly demonstrate the Commutative Property?(1 point)

Question

Responses

3x(9y+6)=(3x+9y)⋅6
3 x left parenthesis 9 y plus 6 right parenthesis equals left parenthesis 3 x plus 9 y right parenthesis times 6

3x⋅9y⋅6=162xy
3 x times 9 y times 6 equals 162 x y

3x⋅9y⋅6=9y⋅6⋅3x
3 x times 9 y times 6 equals 9 y times 6 times 3 x

3x⋅9y⋅6=9y+6+3x
3 x times 9 y times 6 equals 9 y plus 6 plus 3 x

Answer 1

The Commutative Property states that the order of addition or multiplication does not affect the result.

Looking at the expressions provided:

1. \( 3x(9y + 6) = (3x + 9y) \cdot 6 \): This expression does not demonstrate the Commutative Property; it rather shows the distributive property.

2. \( 3x \cdot 9y \cdot 6 = 162xy \): This expression shows the result of multiplying all the terms, but it does not demonstrate the Commutative Property because it does not change the order.

3. \( 3x \cdot 9y \cdot 6 = 9y \cdot 6 \cdot 3x \): This expression demonstrates the Commutative Property because it rearranges the factors of multiplication, showing that the order does not matter.

4. \( 3x \cdot 9y \cdot 6 = 9y + 6 + 3x \): This expression is incorrect as it involves addition, which does not pertain to the multiplication shown on the left side.

Therefore, the only expression that correctly demonstrates the Commutative Property is:

3x⋅9y⋅6=9y⋅6⋅3x