# 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 = l^{2}, where * l* is the side of the square.

Volume of the cube: V = a^{3}, 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**: x^{2}^{}

A number to the** cube**: x^{3}^{}

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) = 2r

r = 5 cm. L (5)= 2** · ** cm

S(l) = l^{2}

l = 5 cm A(5) = 5^{2} = 25 cm^{2}

V(a) = a^{3}

a = 5 cm V(5) = 5^{3} = 125 cm^{3}

### 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. **