Use the Associative Property to determine which expression is correctly simplified.
Responses
−3⋅(4x⋅−2)⋅−6y=18−8x
−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)(−2⋅−6y)
−3⋅(4x⋅−2)⋅−6y=−7xy
−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)⋅−2−6y
−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)(−2⋅−6y)
The expression that correctly shows the result of using the Associative Property is:
−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)(−2⋅−6y)
To use the associative property, you need to group the terms in a way that allows for easy multiplication. In this case, we have three factors: -3, (4x)(-2), and -6y.
Let's look at each expression and simplify them:
-3⋅(4x⋅−2)⋅−6y => Start by simplifying the inner parenthesis: (4x)(-2) = -8x. Then, we multiply -3 with -8x and -6y: -3 * -8x = 24x and 24x * -6y = -144xy. Therefore, the expression simplifies to -144xy.
-3⋅(4x⋅−2)⋅−6y=(−3⋅4x)(−2⋅−6y) => This expression shows the associative property correctly applied. We still simplify the inner parenthesis: (4x)(-2) = -8x. Then, we multiply -3 and -2 * -6y: -3 * -2 = 6 and 6 * -6y = -36y. Therefore, the expression simplifies to -36y(4x) = -144xy.
-3⋅(4x⋅−2)⋅−6y=−7xy => This expression is not simplifying correctly using the associative property. The multiplication between -3 and -6y is incorrect.
-3⋅(4x⋅−2)⋅−6y=(−3⋅4x)⋅−2−6y => This expression is not correctly applying the associative property. The terms -2 and -6y should be grouped within the parenthesis.
Therefore, the correct simplified expression using the associative property is: -3⋅(4x⋅−2)⋅−6y=(−3⋅4x)(−2⋅−6y).