The expression \((3x + 4)(3x - 5)\) can be expanded using the distributive property:

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

Expanding each term:

\[
= 9x^2 - 15x + 12x - 20
\]

Now, combine like terms:

\[
9x^2 - 3x - 20
\]

So, the expanded form of the expression is \(9x^2 - 3x - 20\).

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Here are 8 related questions:
1. How would you factor the expression \(9x^2 - 3x - 20\)?
2. What are the roots of the quadratic equation \(9x^2 - 3x - 20 = 0\)?
3. What is the vertex of the quadratic function \(y = 9x^2 - 3x - 20\)?
4. How does the coefficient of \(x^2\) affect the graph of \(y = 9x^2 - 3x - 20\)?
5. Can the expression \(9x^2 - 3x - 20\) be factored using integers?
6. What is the axis of symmetry for the function \(y = 9x^2 - 3x - 20\)?
7. How would you complete the square for the expression \(9x^2 - 3x - 20\)?
8. How would you solve the equation \((3x + 4)(3x - 5) = 0\)?

**Tip:** When working with quadratic expressions, it's helpful to keep track of the middle term (the coefficient of \(x\)) to simplify the process of combining like terms.

Learn how to expand and simplify the expression (3x + 4)(3x - 5) using the distributive property with this detailed step-by-step solution. This problem covers algebraic concepts such as polynomials and quadratic equations. Suitable for Grades 7-9 students.

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