Final answer:
The student can rearrange the terms in the algebraic expression ax - by - ay - bx due to the commutative property of addition and subtraction, which means the order of terms does not affect the final result.
Step-by-step explanation:
The student posed a question about rearranging terms in an algebraic expression, specifically ax - by - ay - bx. The correct response to whether the student can rearrange these terms is A. Yes, because addition and subtraction are commutative operations. For example, the commutative property states that A + B = B + A, which applies to both numbers and vectors, indicating that the order in which you add (or subtract) does not affect the final result. Therefore, rearranging the terms in ax - by - ay - bx to any order will yield the same result after simplification. However, it's important to note that while the addition and subtraction of scalar quantities are commutative, operations like the cross product in vector algebra are not commutative and care must be taken to preserve the original order.