Let's solve the problem step-by-step.
1. Given the length of the side of the square:
[tex]\[
\text{side length} = 3x - y
\][/tex]
2. We need to find the area of the square. The area of a square is given by the square of its side length:
[tex]\[
\text{Area} = (\text{side length})^2
\][/tex]
3. Substitute the side length:
[tex]\[
\text{Area} = (3x - y)^2
\][/tex]
4. Now, we need to expand this expression. Recall the algebraic expansion formula for squaring a binomial:
[tex]\[
(a - b)^2 = a^2 - 2ab + b^2
\][/tex]
In this case, [tex]\(a = 3x\)[/tex] and [tex]\(b = y\)[/tex].
5. Apply the formula:
[tex]\[
(3x - y)^2 = (3x)^2 - 2(3x)(y) + (y)^2
\][/tex]
6. Calculate each term:
- [tex]\((3x)^2 = 9x^2\)[/tex]
- [tex]\(-2(3x)(y) = -6xy\)[/tex]
- [tex]\((y)^2 = y^2\)[/tex]
7. Combine the terms:
[tex]\[
(3x - y)^2 = 9x^2 - 6xy + y^2
\][/tex]
8. Write the final expression for the area:
[tex]\[
\text{Area} = 9x^2 - 6xy + y^2
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{9x^2 - 6xy + y^2}
\][/tex]
