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Introduction to Algebra


Algebra is that branch of mathematics, which includes the study of the expressions containing the variables and the constants. Here we are going to learn about Introduction to Algebra. While talking about Intro to Algebra, we Mean the basic knowledge of the variables and their mathematical Relations with different operators. Algebra Introduction includes the basic study of the use of the operators and how the different values of the variables effect the given equations of algebra.

If we have some equality with the left and the right side of the equation, we say that in order to find the value of the variable, we will use hit and trial method, by which we check the left side of the equation and the right side of the equation are equal or nit. In case we have both the sides of the equations as equal, it indicates that the particular value of the variable satisfies the equation. In case the two sides of the equation are not equal, then we say that the particular value does not satisfy the equation.

Now we look at the following equation, 3x + 5 = 8;
So we say that the variable x is unknown, and then if we need to find the value of the value of the unknown variable in the equation, it means that we go on trying different values of ‘x’ and check by which value, the left side of the equation is equal to the right side of the equation. So we start with x = 0
3 * 0 + 5 = 0 + 5 = 5,
So this time it is not equal to the right side of the equation. Thus x = 0 is not the solution. Now we try for x = 1, so 3 * 1 + 5 = 3 + 5 = 8.
So LHS = RHS, so x= 1 is the solution.

Definition of Algebra

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The definition of Algebra, can be given as “a branch of mathematics which is use to put the letters in place of numbers”. Algebra definition covers several topics like the Real Numbers, complex numbers, matrices, vectors, etc. We will use letter like (P or Q) in place of the given unknown values. For example: “y + 4 = 9”; Here in the given expression ‘y’ is unknown variable. Now, we have to find the value of ‘y’ by subtracting 4 on both sides of the expression. So we can write it as:
= y + 4 = 9;
= y + 4 - 4 = 9 – 4;
= > y = 5; so the value of y is 5.

As we know algebra definition focus on several topic one of them is ‘algebraic expression’. To discuss the algebraic expressions, it is necessary to know about expressions and algebra, in the expressions we include one or more symbols, variables and constants but they all have finite value. So, we can say that the algebraic expression is the Combination of the alphabets, numbers, basic arithmetic symbols. It is not necessary that algebraic expressions have basic arithmetic symbols.

Example: - 4s, 8t, s – t, -8u / 6, 4s + 9t
In the above examples s, t, u are the letters or alphabets, 4, 6, 8, 9 are the numbers and -, + are the basics arithmetic symbols or signs. Some part of an algebraic expressions separated by + or - operation are known as terms of the expression. Now we will see the types of Algebraic Expressions. There are three types of algebraic expression which are shown below.
1. If a polynomial containing one non- zero term is known as monomial.
For example: 4x2, 9xyz.
2. If a polynomial containing two non- zero term is known as binomials.
For example: 7 + 9x, 4a + 6b2.
3. If a polynomial containing three non- zero term is known as trinomials. For example: 8 + 7x – 4y, a2 + b3 - 6c.
This is a brief introduction of what is algebra?