Final answer:
The length of one side of the square is the square root of the area expression. For Marta's square, doubling the side length from 4 inches to 8 inches results in an area four times larger because the area of a square scales by the square of the scale factor.
Step-by-step explanation:
The expression that represents the length of one side of the square with an area of [4-4x+x^2] square meters is found by taking the square root of the area, as the area of a square is given by the side length squared. In the case of Marta's squares, initially, she has a square with a side length of 4 inches. If a similar square has dimensions that are twice the first square, the side length of the larger square is calculated as: 4 inches x 2 = 8 inches. Therefore, the area of the larger square is the square of the new side length, so the area of the larger square is 8 inches x 8 inches = 64 square inches, which is 4 times the area of the smaller square, as the area of a square scales by the square of the scale factor.