To determine which expressions are equivalent using the Associative Property, we first need to simplify the left side of the first expression, \(-3 \times (4x \times -2) \times -6y\).
- Simplify the left side: \[ -3 \times (4x \times -2) \times -6y \] Start with \(4x \times -2\): \[ 4x \times -2 = -8x \] Now substitute that back into the expression: \[ -3 \times (-8x) \times -6y \] Next, simplify \(-3 \times -8x\): \[ -3 \times -8x = 24x \] Now, multiply by \(-6y\): \[ 24x \times -6y = -144xy \]
So, the left side simplifies to \(-144xy\).
Now let's analyze the right side of each expression to see if any of them simplify to \(-144xy\).
Expressions to Evaluate:
-
First Expression: \[ (-3 \times 4x) \times -2 - 6y \] This can be interpreted as: \[ (-12x) \times -2 - 6y = 24x - 6y \] This does not equal \(-144xy\).
-
Second Expression: \[ (-3 \times 4x) \times (-2 \times 6y) \] First calculate \( -2 \times 6y = -12y\): \[ (-12x) \times -12y = 144xy \] This does not equal \(-144xy\).
-
Third Expression: \[ -7xy \] This clearly does not equal \(-144xy\).
-
Fourth Expression: \[ 18 - 8x \] This does not equal \(-144xy\).
Summary of Evaluation:
None of the given expressions simplify to \(-144xy\).
Thus, none of the expressions are equivalent to the left side.
3 answers