To determine the expression that represents the area of a fabric square, we start by noting the given length of a side of the fabric square: [tex]\( x + 4 \)[/tex].
The area of a square is calculated by squaring the length of one of its sides. Therefore, we need to square the expression [tex]\( x + 4 \)[/tex].
Step-by-step process:
1. Write down the expression for the side length of the fabric square:
[tex]\[ x + 4 \][/tex]
2. To find the area of the square, we square this expression:
[tex]\[ (x + 4)^2 \][/tex]
3. Next, we expand the squared expression:
[tex]\[ (x + 4)^2 = (x + 4)(x + 4) \][/tex]
4. Use the distributive property (also known as the FOIL method for binomials) to expand the product:
[tex]\[ (x + 4)(x + 4) = x \cdot x + x \cdot 4 + 4 \cdot x + 4 \cdot 4 \][/tex]
[tex]\[ = x^2 + 4x + 4x + 16 \][/tex]
5. Combine like terms:
[tex]\[ x^2 + 4x + 4x + 16 = x^2 + 8x + 16 \][/tex]
Thus, the expression that represents the area of a fabric square is:
[tex]\[ \boxed{x^2 + 8x + 16} \][/tex]
