If the length of the side of a square is [tex]3x - y[/tex], what is the area of the square in terms of [tex]x[/tex] and [tex]y[/tex]?

A. [tex]9x^2 - 2xy + y^2[/tex]

B. [tex]3x^2 - 6xy + y^2[/tex]

C. [tex]9x^2 + 6xy - y^2[/tex]

D. [tex]9x^2 - 6xy + y^2[/tex]



Answer :

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]