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!