In this module; we will study algebraic expression definition. But before studying algebraic expressions; we should know what algebra is, what are constants and what are variables?

 

Algebraic Expression Definition

 

Let us start with algebra. Algebra is a language of symbols. The symbols can include numbers, letters, characters, and operation signs.

 

Where numbers mean constants, letters and characters are variables, like a, b, c, x, y, z, alpha, beta, theta, and �meu� etc. And operation signs are plus, minus, multiplication, and division.

 

What are variables and constants?

 

Now, let us understand, what are variables and constants. Variables are symbols used in algebra to represent a number.

 

To understand algebraic expression definition clearly, we can take an example of a rectangle.

 

Let L and W be the length and width of a rectangle. Here, L and W can be replaced with any constants. In first case, if we take L = 5 cm and W = 3 cm, in second case, L = 2 m and W = 6 m and in the third case L = 4 m and W is also 4 m. We see that in all three cases the dimensions are different. This is just an example to understand; what is a variable.

 

 

Also constant is a fixed value that cannot be changed.

For example; The length and width of a rectangle are 6 m and 4 m respectively. Here, the dimensions are fixed, they cannot be changed so 6 and 4 are constants.

 

 

Now, we will learn, how are expressions Formed?

 

An expression is a finite combination of symbols that are well-formed according to the rules applicable in the context. Symbols can designate values (constants), variables, operations, relations, or can constitute punctuation or other syntactic entities.

 

For example; the expression 4x + 5 is obtained from the variable x, first by multiplying x by the constant 4 and then adding the constant 5 to the product.

 

Example: Look at how the following expressions are obtained: 2x², 3xy + 11

 

Solution:

 

(i) By multiplying x with x we obtain x² and then we multiply x² by the constant 2.

 

2x² = 2*x*x

 

(ii) In 3xy + 11, we first obtain xy, multiply it by 3 to get 3xy and add 11 to 3xy to get the expression. 3xy + 11 = 3 * x * y + 11

 

Read More:
Types Of Algebraic Expressions: Monomial, Binomial, Trinomial and Other