# Algebraic Expressions

Algebra is the handling of numerical relations in which one or more quantities are unknown. These terms are called variables or unknowns and they are represented by letters.

An algebraic expression is a combination of letters and numbers linked by the signs of operations: addition, subtraction, multiplication, division and exponentiation.

The algebraic expressions allow us, for example to find areas and volumes.

Length of the circumference: L = 2 r, where r is the radius of the circumference.

Area of the square: S = l2, where l is the side of the square.

Volume of the cube: V = a3, where a is the edge of the cube.

### Common Algebraic Expressions

The double of a number: 2x

The triple a number: 3x

The quadruple of a number: 4x

Half of a number: x/2.

A third of a number: x/3.

A quarter of a number: x/4.

A number is proportional to 2, 3, 4, ...: 2x, 3x, 4x,...

A number to the square: x2

A number to the cube: x3

Two consecutive numbers: x and x + 1.

Two consecutive even numbers: 2x and 2x + 2.

Two consecutive odd numbers: 2x + 1 and 2x + 3.

Break 24 in two parts: x and 24 − x.

The sum of two numbers is 24: x and 24 − x.

The difference of two numbers is 24: x and 24 + x.

The product of two numbers is 24: x and 24/x.

The quotient of two numbers is 24; x and 24 · x.

### Numerical Value of an Algebraic Expression

The numerical value of an algebraic expression for a particular value is the number obtained by replacing the unknown values with the numerical value given and perform the operations.

L(r) = 2 r

r = 5 cm.         L (5)= 2 · cm

S(l) = l2

l = 5 cm        A(5) = 52 = 25 cm2

V(a) = a3

a = 5 cm         V(5) = 53 = 125 cm3

### Types of Algebraic Expressions

#### Monomial

A monomial is an algebraic expression formed by a single term.

#### Binomial

A binomial is an algebraic expression formed by two terms.

#### Trinomial

A trinomial is an algebraic expression formed by three terms.

#### Polynomial

A polynomial is an algebraic expression consists of more than one term.