Algebraic Expressions and their Components

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Introduction to Algebraic Expressions and their Components

What are algebraic expressions? Well, simply put, they are language statements converted into mathematical form to give them universal understanding.  Let’s take an example to make it easier:

English Statement: “I have 3 different kinds of fruit. 2 pieces of the first kind, 1 piece of the second and 3 of the third.”

Algebraic Expressions: “2x + y + 3z” fruits in the bag.
 

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The Big Idea: What constitutes an algebraic expression?

Every mathematical expression has certain elements. The five key elements of an algebraic expression are the variables, the power, the coefficients, the number constants, and the operators.

How to build an algebraic expression

Let’s recap. The entire purpose of algebraic expressions is to help convert spoken word into mathematical statements. Before we jump to the how, it is best to familiarize ourselves with some of the terminologies used to describe specific operations:

Enough reading about what is to be done, it’s time to get down and get your hands dirty. Here, try solving these simple word-based problems that require you to construct your an algebraic expression:

Types of algebraic expressions

Depending on the number of terms in an algebraic expression, there are mainly three types of algebraic expressions that we commonly use use.

Like Terms

When working with algebraic expressions, certain terms with the same variable can be added or subtracted to simplify the expression. These terms, which have the same variables are called Like Terms.

Simplification of algebraic expressions

When there are complex expressions of many terms, then more sophisticated methods like factorisation are used to simplify those terms. But for now, we will look at simple ways of making the expression easier to operate on.

  • In an algebraic expression, there might be more than one instance of a like term occurring. A like term is an expression which has the same variable and the same power. So, in the expression \({5x – 3y + 3x – 7,}\) there are four terms, but out of them, two are like terms. So, we can simplify them to write the expression as \({8x – 3y – 7.}\)

  • If a term is written \({3x^2 \over 2x,}\) then the powers of \({x}\) can be simplified, and the term can be written as \({3x \over 2}\).

  • This will be dealt with in more detail when we discuss factorisation, but it is also possible to take out the common factor from two or more terms of an algebraic expression if it helps in the simplification. So the expression \({3x – 2x^2y + 4xy^2 – 7y}\) can also be written in this way \({3x – 2x^2y + 4xy^2 – 7y=3x - 2xy(x-2y) – 7y}\).

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