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Which expressions correctly demonstrate the Commutative Property?(1 point) Responses 3x⋅9y⋅6=162xy3𝑥⋅9𝑦⋅6=162xy 3 x times 9 y times 6 equals 162 x y 3x⋅9y⋅6=9y⋅6⋅3x3𝑥⋅9𝑦⋅6=9𝑦⋅6⋅3𝑥 3 x times 9 y times 6 equals 9 y times 6 times 3 x 3x(9y+6)=(3x+9y)⋅63𝑥(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=9y+6+3x

1 answer

The Commutative Property states that the order in which two numbers are added or multiplied does not change the result.

From the given expressions, the ones that correctly demonstrate the Commutative Property are:

  1. \(3x \cdot 9y \cdot 6 = 9y \cdot 6 \cdot 3x\)

This expression shows that the multiplication is rearranged (commuted).

The other expressions do not correctly demonstrate the Commutative Property. For instance:

  • \(3x(9y+6) = (3x+9y) \cdot 6\) involves distribution and does not illustrate commutation.
  • \(3x \cdot 9y \cdot 6 = 9y + 6 + 3x\) changes a multiplication expression into a sum, which does not reflect the commutative property.

So, the only correct answer is:

\(3x \cdot 9y \cdot 6 = 9y \cdot 6 \cdot 3x\).