Algebraic Expressions and Equations

Algebra is a branch of Mathematics that allows us to express our daily life situations in the form of numbers and letters (variables). It involves solving equations to find the values of the variables involved.


Before we discuss algebra, it is important to revise the basics.


First, you need to have an understanding of the arithmetic processes addition, subtraction, multiplication, and division. These need to be clear in order to algebra.

Next, remember the key to operations i.e. BODMAS.


B is for brackets,

O is for order,

D is for division

M is for multiplication

A is for addition and 

S is for subtraction. 


Solving equations in the order of this key. 


Finally, make sure you understand how negative numbers work. This includes knowing what happens when you add, subtract, multiply, or divide negative numbers with one another.


After this, we can proceed with what are algebraic expressions? To understand it we need to know what an expression is and what an equation is and how they differ.


Algebraic Expressions Definition

An algebraic expression refers to a mathematical statement consisting of numbers, variables, and with an arithmetic operation between them. These variables can take on any value.


Variable is anything that varies. In an expression, the variables are represented by alphabetical letters like a, b, c, m, n, p, x, y, z, etc. Using a combination of letters and numbers numerous expressions can be made. Since now we know the definition of the algebraic expression, let's understand it better with a few examples.


Algebraic Expressions Examples

Here are some examples of an expression:

  • 3x+5y-10

  • 2x+10

  • 3x+2y

What does it Mean to Simplify Algebraic Expressions?

Simplifying expressions means finding a simplified version of the given expression. In addition to knowing the order of operations, we need to know how to combine the like terms, how to factor a number in order to factor or simplify the expression.


You collect the like terms, i.e. the variables with the same degree and then combine them. Separate the constant terms and simplification is done.


For example, let’s simplify this expression


4m + 4 + 3m + 2


First, put the like terms together i.e. the numbers with the same variable together and constants  and operate them:

4m + 3m = 7m and 

4 + 2 = 6

So, the simplified expression is 7m + 6.

This is how to simplify algebraic expressions of any kind.


Algebraic Equations Definition

An algebraic equation is an expression with two sides connected by the equal sign (=). There is a left-hand side (LHS) and right-hand side (RHS) with an equal sign in the middle. This means that LHS is equal to the RHS of the expression.


Any expression without an equal sign is not an equation. For example, 20x + 63 > 10, is not an equation. Every equation is an expression but every expression is an equation.

Let’s look at some algebraic equations examples:

  • 8m + 6 = 13n - 4

Here the LHS= 8m + 6 and the RHS= 13n - 4.

  • 3x - 5y = 77

Here the LHS= 3x - 5y and RHS= 77.


The equation remains the same if you interchange the LHS and RHS.


Steps to Solving Algebraic Equations

The purpose of solving equations is to find the values of the variables in the algebraic expressions and equations.


The first step is to isolate the variable terms together and the constants together. This means putting each on one side (LHS and RHS).


After isolating them, apply arithmetic operations such as addition, subtraction, multiplication, division on each side. Some equations may also need-finding squares or square roots.


Algebraic Expression and Equation Solved Question

Here is an example of how to solve algebraic equations.


Question: Find the value of x in the given equation: 5x + 10 = 90


Solution:

Given Equation: 5x + 10 = 90

  1. Separate the variable and the constant term:

Shift the variable terms on the left side and the constants on the right.

So it will be:

5x = 90-10

  1.  Perform the arithmetic operation, which in this case is subtraction 

5x = 80

  1. Perform the next arithmetic operation i.e. division in this case

x = \[\frac{80}{5}\] 

⇒ x = 16

Therefore, the value of x is 16.


Did you know?

  • The roots of an algebraic expression problem have been found in Egypt and Babylon, dating back to 1900 BC! 

  • The word ‘algebra’ originates from a Latin variant of Arabic word al-jabr, given by Mathematician Mohammed ibn-Musa al-Khowarizmi in 825 A.D.

  • The signs of (+) and (-) used in performing algebraic equations were discovered in the 16th century. Before that, people use written words to express the functions of addition and subtraction.

  • Algebra is used thoroughly in the fields of engineering, medicine, economics, mathematics, etc. You can find it everywhere!

We have covered in this article what algebraic expressions, and what is the algebraic equation.  Algebra is something you get better at with practice. Continue to sharpen your math skills and you will master it!

FAQ (Frequently Asked Questions)

Q1. What are Monomials and Polynomials?

Answer: Both monomial and polynomials are algebraic equations containing variable and constant terms with whole-number exponents. The distinction is that monomials have one term, whereas polynomials have more than one term. For example, 5ab is a monomial in algebraic expression.


You can also classify polynomials by degree. A slight change in the number of the exponent can lead to the change of the course of the algebraic expressions. Polynomials with one degree are called linear, with two are called quadratic and three are cubic polynomials. The equation x² - 6x - 3 is called a quadratic polynomial. Quadratic equations are commonly found in algebra.