To expand the expression \((2x + 2)(x - 9)\), we will apply the distributive property (also known as the FOIL method for binomials).

1. First, multiply the first terms:  
   \(2x \times x = 2x^2\)

2. Next, multiply the outer terms:  
   \(2x \times -9 = -18x\)

3. Then, multiply the inner terms:  
   \(2 \times x = 2x\)

4. Finally, multiply the last terms:  
   \(2 \times -9 = -18\)

Now, combine all these terms together:  
\[
2x^2 - 18x + 2x - 18
\]

Combine like terms:  
\[
2x^2 - 16x - 18
\]

So, the expanded form of \((2x + 2)(x - 9)\) is:
\[
2x^2 - 16x - 18
\]

Would you like more details or further explanation?

Here are 5 related questions you might want to consider:
1. How do you factor quadratic expressions like \(2x^2 - 16x - 18\)?
2. What are the solutions to \(2x^2 - 16x - 18 = 0\)?
3. Can you simplify \((2x + 2)(x - 9)\) further if given specific values of \(x\)?
4. How does the distributive property work with trinomials?
5. What happens when you apply the FOIL method to different types of binomials?

**Tip**: Always combine like terms after distributing to simplify your expression fully!

Learn how to expand and simplify the expression (2x+2)(x-9) step-by-step using the distributive property. This solution covers key algebraic concepts, including multiplying binomials and combining like terms. Perfect for students in Grades 8-10 looking to strengthen their understanding of algebra.

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