What is the opposite operation of multiplication in algebraic terms?

The correct answer is factoring because it serves as the inverse operation to multiplication in algebra. Multiplication can be viewed as combining groups of equal size, whereas factoring involves breaking down a product into its constituent factors. For example, when you multiply numbers together, like 3 and 4 to get 12, factoring allows you to take the product (12) and express it as the multiplication of its factors (3 and 4). This relationship illustrates how factoring essentially "undoes" multiplication, making it the opposite operation in this context.

Adding, although related to a different aspect of arithmetic operations, does not serve as an inverse to multiplication. While both addition and multiplication are fundamental operations, they operate independently of each other in terms of their inverse relationships. Substituting is a technique often used in solving equations or simplifying expressions but does not have any direct relationship to the operations of multiplication or their opposites. Expanding refers to distributing multiplication over addition, which again is not an inverse operation but a way to reformat expressions involving multiplication.