In a visual model, (25x^2-1) is rearranged into a long rectangle. What will the rectangle sides be?

Correct answer: (5x-1) and (5x+1) / sides

The correct answer is A: (5x-1) and (5x+1). Recognize 25x^2 as (5x)^2 and 1 as 1^2. Thus the expression is a difference of two squares: (5x)^2-1^2. Using p^2-q^2=(p-q)(p+q), with p=5x and q=1, we obtain (5x-1)(5x+1). In the rearranged visual model, these two factors become the rectangle's side lengths. Option A is correct because multiplying the sides gives 25x^2-1. Option B would multiply to 625x^2-1, so it uses 25x instead of its square root, 5x. Option C gives (5x-1)(x+1), whose leading term is 5x^2 and therefore cannot match 25x^2. Option D is a square of (5x+1), producing positive middle and constant terms, not a difference. Memory cue: for U^2-V^2, take the difference and sum of the square roots.