# Variables, Constants and Expressions

In any particular mathematical problem or situation, we can talk about the following two types of entities:

(a) **Variables:** a variable is an entity whose value is not fixed; it can vary. Variables are generally denoted by the letters *x*, *y*, *z* etc.

(b) **Constants:** a constant is an entity whose value is fixed for the given situation. The value of the constant might be *unknown*, but we know that it is *fixed*. Constants are generally denoted by the letters *a*, *b*, *c*, *p*, *q* etc if their values are not known or not provided, and by specific numerical values (like 3, \(\pi\) etc) if their values are known.

An **expression** is a composite entity formed by combining variables and constants using various mathematical operations. Let’s see some examples of expressions, and list the variables and constants occurring in them:

Expression |
Variables |
Constants |

\(2\) | None | \(2\) |

3\(x\)+7 | \(x\) | 3,7 |

\(ax^2+\;bx\;+\;c\) | \(x\) | \(a,b,c,2\) |

\(\sqrt x+2^{y\;}+\;c^x\) | \(x,y\) | \(2,c\) |

\(\frac1{\sqrt{x+2}}+ay+\mathrm{πz}\) | \(x,y,z\) | \(1,2,a,\pi\) |