To determine which expressions are equivalent using the Associative Property, we need to understand what the property states. The Associative Property refers to how you group numbers in addition or multiplication doesn't change their result. It applies to expressions involving multiplication and also to addition.
Let's break down the expressions:
A. \(-3*(4x*-2)*-6y\) vs \(18-8x\)
B. \(-3*(4x*-2)*-6y\) vs \(-7xy\)
C. \(-3*(4x*-2)-6y\) vs \((-34x)*-2-6y\)
D. \(-3*(4x*-2)-6y\) vs \((-34x)(-2*-6y)\)
First, let's simplify \(-3*(4x*-2)*-6y\).
- Calculate \(4x * -2 = -8x\).
- Now compute \(-3 * -8x = 24x\).
- Finally, multiply by \(-6y\): \(24x * -6y = -144xy\).
So, \(-3*(4x*-2)*-6y = -144xy\).
Now we need to check each of the other expressions:
A:
- Compare \(-144xy\) to \(18 - 8x\).
- These are not equivalent.
B:
- Compare \(-144xy\) to \(-7xy\).
- These are not equivalent.
C:
- The expression \((-34x)-2-6y\) simplifies as follows:
- First compute \((-3 * 4x) = -12x\).
- Then \(-12x * -2 = 24x\).
- Now apply \(-6y\): This does not lead to the expression being equal to \(-144xy\).
- Thus, they are not equivalent.
D:
- Now for \((-34x)(-2-6y)\):
- Calculate \(-3*4x = -12x\).
- Calculate \(-2*-6y = 12y\).
- So, now multiply \(-12x * 12y = -144xy\), which does indeed equal \(-144xy\).
This means that D is equivalent to the original expression.
In conclusion:
- A: Not equivalent
- B: Not equivalent
- C: Not equivalent
- D: Equivalent
Thus, the only expression that is equivalent to the original is D.
3 answers