Final answer:
The correct algebraic expression to represent the product of 10 and the difference of 5y and 1 is 10 * (5y - 1), which suggests the factors are 10 and (5y - 1).
Step-by-step explanation:
The student is asked to find the algebraic expression representing the product of 10 and the difference between 5y and 1. The correct expression for this operation is 10 * (5y - 1), which corresponds to option b. The factors in this expression are 10 and (5y - 1). Option a expands the multiplication incorrectly, assuming the difference is only applied to the 1, while c and d are incorrect as they don't represent the product of 10 and the difference of 5y and 1 as a single entity.
Understanding algebraic expressions is crucial in solving equations efficiently. When we look at the multiplication and subtraction rules, remember that the difference should be calculated first due to the order of operations, known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).