Question

Use the Associative Property to determine which expressions are equivalent.(1 point)
Responses

−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)⋅−2−6y

negative 3 times left parenthesis 4 x times negative 2 right parenthesis times negative 6 y equals left parenthesis negative 3 times 4 x right parenthesis times negative 2 minus 6 y

−3⋅(4x⋅−2)⋅−6y=−7xy

negative 3 times left parenthesis 4 x times negative 2 right parenthesis times negative 6 y equals negative 7 x y

−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)(−2⋅−6y)

negative 3 times left parenthesis 4 x times negative 2 right parenthesis times negative 6 y equals left parenthesis negative 3 times 4 x right parenthesis left parenthesis negative 2 times negative 6 y right parenthesis

−3⋅(4x⋅−2)⋅−6y=18−8x

negative 3 times left parenthesis 4 x times negative 2 right parenthesis times negative 6 y equals 18 minus 8 x

Answer 1

Only the third expression is equivalent.

Reason: −3·(4x·−2)·−6y = −3·(−8x)·−6y = −144xy. Grouping as (−3·4x)(−2·−6y) is allowed by the associative property and also equals −144xy. The other choices are not equivalent.