Final answer:
Adi's algebra tile configuration for (-2x - 1)(2x - 1) shows some incorrectly labeled tiles based on the rules of signs in multiplication, making option C (The signs on some of the products are incorrect) the correct answer.
Step-by-step explanation:
The student asked which statement is true regarding Adi's use of algebra tiles for the product (-2x - 1)(2x - 1). To find the correct answer, we must apply the rules of signs in multiplication to the tiles chosen by Adi. For multiplying two negative numbers, the result should have a positive sign. In Adi's configuration, there appear to be algebra tiles that are labeled incorrectly based on the described factors.
Firstly, we need to verify the product of the given factors algebraically:
Minus x times plus x gives minus x squared.
Minus x times minus 1 gives plus x.
Minus 1 times plus x gives minus x.
Minus 1 times minus 1 gives plus 1.
After multiplying, we should have the tiles show the algebraic expression 4x^2 + 4x - 1, where the sign follows the rules as previously mentioned. In Adi's product spot, the signs on some products are incorrect according to the rules.
Therefore, the correct answer to the question is that the signs on some of the products are incorrect, which corresponds to option C: The signs on some of the products are incorrect.