What is a literal expression?

Why use letters in maths?

In algebra, we replace unknown numbers or variables with letters: x, y, a, b, n… This allows us to write a rule that applies to all numbers, without having to rewrite it every time.

Example: the perimeter of a square with side length c is P = 4 × c. This formula works regardless of the side length c, whether c is 3, 10 or 100.

Basic vocabulary

• A literal expression contains at least one letter: 3x + 5, a² - b, 2(x+1)
• A term is a part separated by a + or -: in 3x + 5, the terms are 3x and 5
• A coefficient is the number that multiplies the letter: in 3x, the coefficient is 3

Simplified notation

In algebraic notation, we simplify the writing:

Standard notation	Simplified notation
3 x x	3x
x x y	xy
a x a	a²
5 x (x+2)	5(x+2)
1 x x	x

We never write the symbol ‘x’ immediately before a letter, and we do not place an ‘x’ between a number and a set of brackets.

Common pitfall

Do not confuse 2x (twice x, i.e. x + x) with x^2 (x times x). If x = 3, then 2x = 6 but x² = 9: the result is not the same at all! Always check with a simple numerical example if you’re in any doubt.