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The given expression is \((x - 4)^2\), and we need to expand it to find the correct answer.

### Step-by-Step Expansion:
\[
(x - 4)^2 = (x - 4)(x - 4)
\]

Using the distributive property (FOIL method):

\[
= x(x - 4) - 4(x - 4)
\]

\[
= x^2 - 4x - 4x + 16
\]

Simplify the like terms:

\[
= x^2 - 8x + 16
\]

### The correct answer is: **b)** \(x^2 - 8x + 16\)

Would you like more details or have any other questions?

### Related Questions:
1. How do you expand binomials in general?
2. What is the FOIL method and how does it work?
3. How do you factor expressions like \((x - 4)^2\) back from their expanded form?
4. What other types of quadratic expressions can be factored similarly?
5. How do different signs in the binomial affect the expanded form?

### Tip:
When expanding binomials like \((x - a)^2\), remember the result follows the pattern \(x^2 - 2ax + a^2\).

Learn how to expand (x - 4)^2 and find the correct form. This algebra problem demonstrates binomial expansion using the distributive property and is suitable for students in Grades 8-10.

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