# 1.2 Expressions

An *expression* is a written combination of data with operations to
perform on that data. That sounds quite formal, so imagine a mathematical formula
like:

15 × 6^{2} + 3 × 6 – 4 .

This expression contains six pieces of data: 15, 6, 2, 3, 6, and 4. There are five operations: multiplication, exponentiation, addition, multiplication, and subtraction. If I rewrite this using symbols often used in programming languages, it is:

15 * 6**2 + 3 * 6 - 4

See that repeated 6? Suppose I want to consider different numbers in its place. I can write the formula:

15 × *x*^{2} + 3 × *x* – 4

and the corresponding code expression:

15 * x**2 + 3 * x - 4

If I give *x* the value 6, I get the original expression. If I give it the value 11, I
calculate:

15 * 11**2 + 3 * 11 - 4

We call *x* a *variable* and the process of giving it a value *assignment*.
The expression

x = 11

means “assign the value 11 to *x* and wherever you see *x*,
substitute in 11.” There is nothing special about *x*. I could have used *y* or
something descriptive like *kilograms*.

An expression can contain multiple variables.

Exercise 1.3

In the expression

`a * x**2 + b * x + c`

,

what would you assign to *a*, *b*, *c*, and *x* to
get

`7 * 3**2 + 2 * 3 + 1`

?

What assignments would you do for

`(-1)**2 + 9 * (-1) - 1`

?

The way we write data, operations, variables, names, and words together with the rules for
combining them is called a programming language’s *syntax*. The syntax must be unambiguous
and allow you to express your intentions elegantly. In this chapter, we do not focus on syntax
but more on the ideas and the meaning, the *semantics*, of what programming languages can
do. In Chapter 2, *Working with
Expressions*, we begin to explore the syntax and features of Python.

We’re not limited to arithmetic in programming. Given two numbers *x* and *y*, if
I saw **maximum**(*x*, *y*), I would expect it to return the larger
value. Here “**maximum**” is the name of a *function*. We can write our own
or use functions created, tested, optimized, and stored in libraries by others.