Select the correct answer.

Each side of a square is [tex]\((x-5)\)[/tex] units. Which expression can be used to represent the area of the square?

A. [tex]\(x^2-5x+10\)[/tex]
B. [tex]\(x^2-5x-10\)[/tex]
C. [tex]\(x^2-10x+25\)[/tex]
D. [tex]\(x^2-10x-25\)[/tex]



Answer :

To determine the expression for the area of a square where each side length is [tex]\((x-5)\)[/tex] units, we can follow these steps:

1. Understand the problem: We are given that each side of the square is [tex]\((x-5)\)[/tex] units.

2. Area of a square: The area [tex]\(A\)[/tex] of a square is found by squaring the length of one of its sides. If [tex]\(s\)[/tex] is the side length, then the area [tex]\(A\)[/tex] is given by [tex]\(A = s^2\)[/tex].

3. Substitute the given side length: Here, the side length [tex]\(s\)[/tex] is [tex]\((x-5)\)[/tex]. Substituting [tex]\(x - 5\)[/tex] for [tex]\(s\)[/tex], we get:
[tex]\[ A = (x - 5)^2 \][/tex]

4. Expand the squared binomial: We need to expand the expression [tex]\((x - 5)^2\)[/tex]. Using the binomial expansion formula [tex]\((a - b)^2 = a^2 - 2ab + b^2\)[/tex], we can expand [tex]\((x - 5)^2\)[/tex] as follows:
[tex]\[ (x - 5)^2 = x^2 - 2 \cdot x \cdot 5 + 5^2 \][/tex]

5. Simplify the expression: Calculate each term in the expansion:
[tex]\[ x^2 - 2 \cdot x \cdot 5 + 25 = x^2 - 10x + 25 \][/tex]

6. Look for the matching answer choice: The simplified expression for the area is [tex]\(x^2 - 10x + 25\)[/tex].

Therefore, the correct answer is:
[tex]\[ \boxed{x^2 - 10x + 25} \][/tex]