Which of the following illustrates the commutative property of multiplication? Enter $$ a, b, c, d $$, or $$ e $$. $$ \begin{array}{ll}a \cdot z y=y z & b, a+(c+d)=(a+c)+d \ c \cdot y+a=a+y & d .(d b)(e+f)=d[b(c+f)] \ e \cdot(a c+d c)(e f)=(d c+a c)(e f)\end{array} $$

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The commutative property of multiplication states that changing the order of the factors does not change the product. In mathematical terms, this can be expressed as:

$$
x \cdot y = y \cdot x
$$

Now, let's analyze each option to see which one illustrates this property:

1. **Option a:** $$ a \cdot z y = y z $$
   - This does not clearly show the commutative property as it involves multiple variables and does not explicitly switch the order of multiplication.

2. **Option b:** $$ a + (c + d) = (a + c) + d $$
   - This illustrates the associative property of addition, not multiplication.

3. **Option c:** $$ c \cdot y + a = a + y $$
   - This does not illustrate the commutative property of multiplication; it mixes addition and multiplication.

4. **Option d:** $$ d \cdot (d b)(e + f) = d[b(c + f)] $$
   - This does not illustrate the commutative property of multiplication; it involves distribution and does not switch the order of multiplication.

5. **Option e:** $$ e \cdot (a c + d c)(e f) = (d c + a c)(e f) $$
   - This also does not illustrate the commutative property of multiplication; it involves distribution and does not switch the order of multiplication.

After analyzing all options, none of them clearly illustrate the commutative property of multiplication. However, if we had to choose the one that comes closest, it would be option **a**, but it still does not explicitly demonstrate the property.

Thus, the answer is **a**.
Option **a** illustrates the commutative property of multiplication.

Which of the following illustrates
the commutative property of
multiplication?
Enter , or .

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Which of the following illustrates the commutative property of multiplication? Enter , or .