Final answer:
The correct expression for the total square footage of five carpet remnants is (2 x 8^2) + (3 x 10^2), which calculates the square footage for remnants measuring 8 feet and 10 feet respectively.
Step-by-step explanation:
The expression representing the total square footage for five carpet remnants, where two remnants measure 8 feet on each side and three remnants measure 10 feet on each side, is found by calculating the area of each square remnant and then summing them up. The area of a square is given by the formula side length squared (side x side).
For the two remnants each with 8 feet on a side, their total area is 2 x 82 or 2 x 64 square feet. For the three remnants each with 10 feet on a side, their total area is 3 x 102 or 3 x 100 square feet. The combined total square footage is the sum of these two areas: (2 x 64) + (3 x 100) square feet.