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Let's factor the given expression completely:

\[
(5x + 2)(4x - 9) + (3x - 4)(4x - 9)
\]

### Step 1: Identify common factors
Notice that both terms contain the binomial \((4x - 9)\). So, we can factor out \((4x - 9)\) from both terms:

\[
(5x + 2)(4x - 9) + (3x - 4)(4x - 9) = (4x - 9)\left[(5x + 2) + (3x - 4)\right]
\]

### Step 2: Simplify the remaining expression
Now, simplify the expression inside the brackets:

\[
(5x + 2) + (3x - 4) = 5x + 2 + 3x - 4 = (5x + 3x) + (2 - 4) = 8x - 2
\]

### Step 3: Write the final factored form
Substitute the simplified expression back:

\[
(4x - 9)(8x - 2)
\]

### Step 4: Factor further if possible
We notice that the second binomial \((8x - 2)\) has a common factor of 2:

\[
(8x - 2) = 2(4x - 1)
\]

Thus, the fully factored form of the expression is:

\[
(4x - 9)(2)(4x - 1) = 2(4x - 9)(4x - 1)
\]

### Final Answer:
\[
2(4x - 9)(4x - 1)
\]

Would you like any additional details or have any questions?

Here are some related questions to consider:
1. What does factoring help with in solving equations?
2. Can you think of a situation where grouping terms differently might change the solution process?
3. How can you verify if your factorization is correct?
4. Why is it important to look for common factors first?
5. Can every quadratic expression be factored in this manner?

**Tip:** When factoring, always look for common terms or patterns first, as they can significantly simplify the process.

Factor completely: (5x + 2)(4x - 9) + (3x - 4)(4x - 9)

Learn how to factor the algebraic expression (5x + 2)(4x - 9) + (3x - 4)(4x - 9). This solution involves applying the distributive property and factoring out common binomials. Ideal for students in Grades 9-11.

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