Question

Question content area top
Part 1
Use the indicated property to provide a new expression equal to the given expression.​ Simplify, if possible.
left parenthesis 4 x plus 5 y right parenthesis plus 4 z​; associative
Question content area bottom
Part 1
A.4 x plus 5 y plus 4 z
4 x plus 5 y plus 4 z
B.left parenthesis 4 x plus 5 y plus 4 z right parenthesis
left parenthesis 4 x plus 5 y plus 4 z right parenthesis
C.4 x plus left parenthesis 5 y plus 4 z right parenthesis
4 x plus left parenthesis 5 y plus 4 z right parenthesis
D.left parenthesis 5 y plus 4 x right parenthesis plus 4 z
left parenthesis 5 y plus 4 x right parenthesis plus 4 z

Answer 1

To apply the associative property to the expression \( (4x + 5y) + 4z \), we need to regroup the terms. The associative property states that when adding three or more numbers (or expressions), the way in which they are grouped doesn't change the sum.

Therefore, we can focus on rearranging the terms to show that they can be grouped in different ways.

Here’s the expression:

\[
(4x + 5y) + 4z
\]

Using the associative property, we can regroup it as:

\[
4x + (5y + 4z)
\]

Now, looking at the options given:

A. \( 4x + 5y + 4z \)
B. \( (4x + 5y + 4z) \)
C. \( 4x + (5y + 4z) \)
D. \( (5y + 4x) + 4z \)

Among these, the correct application of the associative property that maintains equivalence with the original expression is Option C:

**C. \( 4x + (5y + 4z) \)**.

This maintains the original sum while showcasing a different grouping.