The question asks which option illustrates the distributive property for the expression $(a + b)(cd)$.

The distributive property states that you multiply each term inside the parentheses by the term outside. In this case:

$(a + b)(cd) = (a \cdot cd) + (b \cdot cd) = acd + bcd$

Looking at the options:

• Option a: $(cd)(a + b)$ does not distribute properly, it reverses the terms.
• Option b: $acd + bcd$ correctly applies the distributive property.
• Option c: $(b + a)(cd)$ is a reordering of terms, but it doesn't affect the operation, so this is not fully distributive.
• Option d: $(a + b)(dc)$ changes the order of multiplication within the parentheses, which does not affect the distributive property, but it's not the typical form.
• Option e: $[ (a + b)c]d$ groups parts of the expression differently.

Therefore, the correct answer is b: $acd + bcd$, which properly distributes both terms of $a + b$ over $cd$.

Would you like a more detailed explanation on how the distributive property works or why the other options are incorrect?

Here are 5 relative questions to expand:

1. How does the distributive property differ from the associative property?
2. Can the distributive property be applied to subtraction as well as addition?
3. How is the distributive property used in solving algebraic equations?
4. What happens if one of the terms is zero in the distributive property?
5. Is the distributive property applicable to division?

Tip: The distributive property is a fundamental tool in algebra that simplifies expressions and solves equations by breaking down complex terms.