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.

Explore how to expand and simplify the expression (2a-1)(8a-5) using the FOIL method and distributive property. This problem demonstrates key algebraic concepts such as binomial expansion and polynomial multiplication. Perfect for students in Grades 8-10.

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