Let's expand the expression $(2a - 1)(8a - 5)$ using the distributive property (also known as FOIL for binomials).

$(2a - 1)(8a - 5)$

First, distribute each term in $(2a - 1)$ to each term in $(8a - 5)$:

$= 2a(8a) + 2a(-5) - 1(8a) - 1(-5)$

Now, perform the multiplications:

$= 16a^2 - 10a - 8a + 5$

Combine the like terms $-10a$ and $-8a$:

$= 16a^2 - 18a + 5$

Thus, the expanded form of $(2a - 1)(8a - 5)$ is:

$16a^2 - 18a + 5$

Would you like more details on any step?

Here are some related questions:

1. How can you factor quadratic expressions like $16a^2 - 18a + 5$?
2. What are the special cases where binomials expand differently?
3. How does the distributive property work in polynomial multiplication?
4. Can you apply this to other binomials such as $(3x + 2)(4x - 1)$?
5. What is the FOIL method and when is it used?

Tip: Always combine like terms at the end of expanding binomials to simplify the expression.