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Variables, Constants and Expressions

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 $$ax^2+\;bx\;+\;c$$ $$x$$ $$a,b,c,2$$ $$\sqrt x+2^{y\;}+\;c^x$$ $$x,y$$ $$2,c$$ $$\frac1{\sqrt{x+2}}+ay+\mathrm{πz}$$ $$x,y,z$$ $$1,2,a,\pi$$