To simplify the expression \((3x - 5)(x - 2)\), we'll apply the distributive property (also known as FOIL for binomials):

1. **First terms**: \(3x \cdot x = 3x^2\)
2. **Outer terms**: \(3x \cdot (-2) = -6x\)
3. **Inner terms**: \(-5 \cdot x = -5x\)
4. **Last terms**: \(-5 \cdot (-2) = 10\)

Now, combine these results:
\[
3x^2 - 6x - 5x + 10 = 3x^2 - 11x + 10
\]

So, the simplified expression is:
\[
3x^2 - 11x + 10
\]

Do you want more details or have any questions?

Here are 5 questions to expand on this:

1. How do you factor quadratic expressions like \(3x^2 - 11x + 10\)?
2. What are the solutions to the quadratic equation \(3x^2 - 11x + 10 = 0\)?
3. How can you graph \(y = 3x^2 - 11x + 10\)?
4. What is the vertex form of \(3x^2 - 11x + 10\)?
5. How do the coefficients affect the shape of the parabola represented by \(3x^2 - 11x + 10\)?

**Tip**: When simplifying expressions, always carefully distribute each term and then combine like terms!

Discover how to simplify the algebraic expression (3x-5)(x-2) step-by-step using the distributive property. This lesson explains the process of expanding binomials and combining like terms, ideal for students in Grades 8-10 studying polynomial multiplication and quadratic expressions.

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