To expand the expression $(5x - 3)(x - 2)$, we use the distributive property (also known as the FOIL method for binomials):

1. First: Multiply the first terms in each binomial: $5x \cdot x = 5x^2$
2. Outer: Multiply the outer terms: $5x \cdot (-2) = -10x$
3. Inner: Multiply the inner terms: $-3 \cdot x = -3x$
4. Last: Multiply the last terms: $-3 \cdot (-2) = 6$

Now, add all these results together:

$5x^2 - 10x - 3x + 6$

Combine the like terms $-10x$ and $-3x$:

$5x^2 - 13x + 6$

So, the expanded form of $(5x - 3)(x - 2)$ is:

$5x^2 - 13x + 6$

Would you like more details or have any questions?

Here are 5 related questions you might ask:

1. How do you factorize quadratic expressions?
2. What is the FOIL method in detail?
3. How do you solve quadratic equations?
4. Can you show an example of completing the square?
5. What are the applications of the distributive property in algebra?

Tip: When expanding binomials, always carefully combine like terms to simplify your final expression.