To find the product of [tex]\((x - 3)^2\)[/tex], follow these steps:
1. Understanding the problem: We need to expand the expression [tex]\((x - 3)^2\)[/tex].
2. Expand the expression:
[tex]\(
(x - 3)(x - 3)
\)[/tex]
3. Apply the distributive property (also known as FOIL method for binomials):
[tex]\[
(x - 3)(x - 3) = x^2 - 3x - 3x + 9
\][/tex]
4. Combine like terms:
[tex]\[
x^2 - 3x - 3x + 9 = x^2 - 6x + 9
\][/tex]
So, the product of [tex]\((x - 3)^2\)[/tex] is [tex]\(\boxed{x^2 - 6x + 9}\)[/tex].
Looking at the given options:
- [tex]\(x^2 + 6x + 9\)[/tex]
- [tex]\(x^2 - 9\)[/tex]
- [tex]\(x^2 - 6x + 9\)[/tex]
- [tex]\(x^2 + 9\)[/tex]
The correct answer is:
[tex]\[
x^2 - 6x + 9
\][/tex]
So, the correct choice is:
[tex]\[
\boxed{x^2 - 6x + 9}
\][/tex]
