To solve \((X - 8)(X - 2)\), we'll use the distributive property (also known as FOIL for binomials):

\[
(X - 8)(X - 2) = X \cdot X + X \cdot (-2) + (-8) \cdot X + (-8) \cdot (-2)
\]

Now calculate each term:

\[
X \cdot X = X^2
\]
\[
X \cdot (-2) = -2X
\]
\[
-8 \cdot X = -8X
\]
\[
-8 \cdot (-2) = 16
\]

Now, combine all the terms:

\[
X^2 - 2X - 8X + 16 = X^2 - 10X + 16
\]

So, \((X - 8)(X - 2) = X^2 - 10X + 16\).

Would you like more details on this, or do you have any questions?

### Related questions:
1. How do you factor quadratic expressions like \(X^2 - 10X + 16\)?
2. What is the FOIL method for multiplying binomials?
3. How does the distributive property apply to binomials?
4. Can you apply this method to higher-degree polynomials?
5. How do you expand \((X - a)(X - b)\) for any values of \(a\) and \(b\)?

**Tip:** Always combine like terms (like \(-2X\) and \(-8X\)) after expanding binomials!

Explore how to expand the binomial expression (X - 8)(X - 2) using the FOIL method. This step-by-step solution covers algebraic concepts such as the distributive property and combining like terms. Suitable for students in Grades 8-10.

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