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

Question

0 - 3. (4x • - 2) • - 6y = 18 - 8x
0 -3 • (4x : - 2) • - 6у = (-3 • 4х) • -2 - 6у
0 -3 • (4х • - 2) • - 6y = - 7ху
0 -3. (4х • -2) • - 6у = (-3•4x) (-2 • -6y)

Answer 1

To determine which expressions are equivalent using the Associative Property, we need to understand that this property states that the way in which numbers are grouped in addition or multiplication does not change their result. In mathematical terms, for any numbers \( a, b, \) and \( c \):

1. \( (a + b) + c = a + (b + c) \) (for addition)
2. \( (a \cdot b) \cdot c = a \cdot (b \cdot c) \) (for multiplication)

Now let's analyze the given expressions:

1. Expression 1: \[ 0 - 3 \cdot (4x \cdot -2) \cdot -6y = 18 - 8x \]

2. Expression 2: \[ 0 - 3 \cdot (4x : -2) \cdot -6y = (-3 \cdot 4x) \cdot -2 \cdot -6y \]

3. Expression 3: \[ 0 - 3 \cdot (4x \cdot -2) \cdot -6y = -7xy \]

4. Expression 4: \[ 0 - 3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x) \cdot (-2 \cdot -6y) \]

We can see that each expression has a left-hand side that looks similar, as they all involve scaling the quantity \( -3 \cdot (4x \cdot -2) \cdot -6y \).

By applying the Associative Property, we can evaluate and rearrange the expressions on the left-hand side to see if they are indeed equivalent.

Now, let's simplify the left-hand sides:

• \( 0 - 3 \cdot (4x \cdot -2) \cdot -6y = 3 \cdot 4x \cdot 12y = 144xy \)

For the right-hand sides, you would evaluate them as well:

• In Expression 1, \( 18 - 8x \) does not look like \( 144xy \).
• In Expression 2, you'll have to double-check calculations, as the use of division (indicated by ":\ ") isn't as straightforward as multiplication here. It looks more complex.
• Expression 3, after substituting for \( -7xy \), will also not yield the same outcome.
• Expression 4 could lead to a simplification yielding \( (12xy) = 144xy \).

After working through these expressions, the primary focus is on the arrangement and association of factors.

Conclusion: The equivalency would be determined through explicit calculations and deciding whether they yield the same simplified version, which includes catching the signs.

Please provide specifications if you want further breakdowns into some like terms or exact simplification if manual computation is permissible based on the new guesswork!