b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r)ⁿ as the product of P and a factor not depending on P.

Let's consider a more complex expression: 5x – (2 – 4y). In English, this could be stated as "the difference between 5 times a number and the quantity '4 times another number less than 2'." That's a mouthful, and this expression isn't even that complex! It should be obvious why we do math in symbol notation now: it's much easier to write.

Notice how the English expression mentioned "a number" and "another number." This is a clue that two different variables must be used in the mathematical expression. These two variables might represent two different physical quantities in some situation, and the expression shows how each quantity contributes to the overall behavior.

How many terms are in that expression? Your students will probably say three, but there are only two the way the expression is written. The two terms inside the parentheses are treated as a single thing, so the first term is 5x and the second term is -(2 – 4y). Since there is no number immediately following the minus sign in the second term, we assume the number is actually 1. So the second term could be written as -1(2 – 4y). This should be interpreted as a -1 multiplying everything inside the parentheses.

Of course, we can have expressions which have even more variables, if there are more changing or unknown quantities involved. For example, the compound interest expression P(1 + r)ⁿ has three variables: P, r, and n, each representing a different physical quantity. As written, this expression has only one term, consisting of two factors, P and (1 + r)ⁿ. The first factor depends only on P, while the second depends on r and n.