The expression given is \((8x - 1)(x - y)\). This expression can be expanded by using the distributive property (also known as FOIL—First, Outer, Inner, Last):

\[
(8x - 1)(x - y) = 8x(x) + 8x(-y) - 1(x) - 1(-y)
\]

Now, let's simplify each term:

\[
= 8x^2 - 8xy - x + y
\]

So, the expanded form of the expression \((8x - 1)(x - y)\) is:

\[
8x^2 - 8xy - x + y
\]

Would you like further details or have any questions? Here are some related questions you might find interesting:

1. How does the distributive property work in more complex polynomials?
2. What is the FOIL method, and when is it used?
3. How can you factor an expression like the one we expanded?
4. What are common mistakes to avoid when expanding binomials?
5. How can this expression be used in solving quadratic equations?

**Tip:** Always double-check your work when expanding binomials, especially when dealing with negative signs—they can easily lead to mistakes!

Explore the step-by-step solution to expanding the expression (8x - 1)(x - y) using the distributive property. This problem covers key algebraic concepts, including binomial expansion and the distributive property, and is suitable for students in Grades 8-10.

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