https://file.aiquickdraw.com/mathbot/file/17268489404474mjisocx.jpg

Let's expand and simplify the given expression:

The expression is:

\[
3u(4u + 5) + 3u(5u + 4)
\]

### Step 1: Expand both terms using the distributive property.

\[
3u(4u + 5) = 3u \cdot 4u + 3u \cdot 5 = 12u^2 + 15u
\]

\[
3u(5u + 4) = 3u \cdot 5u + 3u \cdot 4 = 15u^2 + 12u
\]

### Step 2: Add the results.

\[
12u^2 + 15u + 15u^2 + 12u
\]

### Step 3: Combine like terms.

\[
(12u^2 + 15u^2) + (15u + 12u) = 27u^2 + 27u
\]

### Final answer:
\[
27u^2 + 27u
\]

This matches the option in the bottom left: **\(27u^2 + 27u\)**.

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Would you like a detailed breakdown of any step or further clarification?

### Related Questions:
1. How do you distribute terms in binomial expressions?
2. What is the difference between like and unlike terms?
3. How do you simplify expressions after distributing?
4. How do you factor expressions like \(27u^2 + 27u\)?
5. How do you expand when there are more than two terms in parentheses?

### Tip:
Always check your work by re-expanding after simplifying to ensure correctness!

Expand and simplify: 3u(4u + 5) + 3u(5u + 4)

Learn how to expand and simplify the expression 3u(4u + 5) + 3u(5u + 4) using the distributive property and combining like terms. This problem involves core algebraic concepts suitable for students in Grades 6-8.

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