Algebra

       
           
When we list the different branches of the study of mathematics, we find that Algebra is one of the important studies of mathematics. In Maths, Algebra has a very important role to learn and solve many real life problems. When we look at any of the algebraic expression, it is basically the combination of the different terms joined together with the help of the mathematical operators namely addition and subtraction.  A term can have a number along with one or more variables joined with the multiplication and division operation. If we talk about the algebraic expression, it is formed by writing the statement in the form of the mathematical relation.  We will look at the following statement and then observe that how this statement is converted into the mathematical relation of the algebraic terms. This mathematical form of the combination of the terms is called the algebraic expressions.  If we write: 3added to 5 times a square of a number.
Now we know that the number we are talking about is not known, so the first thing while forming the algebraic expression is to form the variables and here let us assume the variable as y.
So the expression is formed as follows:  5 * y^2   + 3
Different mathematical operations can be performed on the algebraic expressions. Let us first look at the rules of addition of the algebraic expressions. Firstly we must know what are like and unlike terms in the algebraic expressions. The terms which have the same degree of all the variables are called like terms. As we say 3x^2 *y and 5 y* x^2 are two like terms and on another hand we have 3x^3 and 3 Y^3 are unlike terms.
Now to add up the algebraic expressions, we will first bring together all the like terms of the   algebraic expressions. The sum of more than two like terms is the sum of the coefficients of the like terms and along with it we write the same variables with the same degrees.
Now we look at the subtraction operation of the algebraic expressions. For this we need to follow the following steps:
1.     Arrange the terms of the given expressions in the same order.
2.     We will write all the terms of the   two expressions in the two rows, such that the like terms appear one under another. We will always remember that we will place the expression to be subtracted in the second row.
3.    Now in the next step, we will change the sign of all the terms, ie. The positive signs are changed to negative and the negative signs are changed to positive.
4.    Now taking into consideration the new signs allotted to all the terms of the second row, we will add up all the terms of the  two rows, remembering the  adding procedure of the like terms.
5.     The result so attained is the difference between the two  given algebraic expressions.

We can even perform multiplication and division operation on the algebraic expressions.

Topics Covered in Algebra

  • Variable
    A symbol which can be assigned different numerical values is known as a variable.  Variables are generally denoted by x, y, z, p, q, r, s, etc.
  • Constant
    A symbol having a fixed value is called a constant, e.g. 8, 5, 9, , a, b, c, etc. are constants. The values of constants remain the same throughout a particular situation, but the 
              Value of a variable can keep changing.
  • Algebraic Expression

    Algebra is a branch of Mathematics in which we use letters of English alphabet to represent some values. As letters do not have any numeric value of their own, they can be assigned any value which is not fixed. Thus, these letters ha...Read More

  • Polynomial
    A polynomial is a mathematical expression consisting of a sum of powers (exponential form) in one or more variables which are multiplied by coefficients. Now we discuss what is polynomial in detail. Polynomial expression are expressions which are...Read More
  • Surface Area and Volume
    Surface area can be defined as total area of faces and curved surface of solid objects or 3 dimensional objects. Square is the unit of area. For example: In case of cube the surface area is 6 * (edge length)2;
    The capacity of a thre...Read More
  • Simple Equations

    By Simple Equations, we mean any of the combination of terms which can be written in the form of an expression. By Simple Math Equations, we mean that we have some of the terms on the left side of equal sign and some of the terms lie on...Read More

  • Quadratic Equations

    Quadratic equations are univariate polynomial equations of second degree and the standard form of Quadratic equation is shown below-

    p x2 + q x + c = 0,

    Here p, q and r are the constants with the condition that ‘p’ is not e...Read More

  • Matrices

    In mathematics matrix or matrices can be defined as a rectangular array of numbers, symbols, or expression. The elements in the matrix are called as the entries of numbers or the words. A matrix can be divided into two parts first is row and se...Read More

  • Determinants

    The determinants definition states that it is a value which is derived in the sense of square matrix. Determinants are calculated by the entries of a square matrix by specified arithmetic term. The determinant is used to provide the importa...Read More

  • Complex Numbers and Quadratic Equations

    A complex number is the number which consists of a real number with imaginary number i. x + y. i is the form of imaginary number. Also we know that the square of the real number is either 0 or positive. Complex nu...Read More

  • Data Handling
    Data handling plays an important role in getting the appropriate results of the data study and analysis. We say that handling data is not any easy task and we must always handle the data with care in order to analyze and come out with the mea...Read More
  • Linear Inequations
    In algebra mathematics a Linear inequation is defined as an inequality which contains a linear function. When two expressions are connected to each other by 'greater than' or 'less than' sign with sign of inequality then we get inequalit...Read More
  • Progressions
    Progression can be defined as arrangement of terms in which sequence of terms follow some conditions. There are different types of progression in maths which are as follows: Arithmetic progression, Geometric progression and Harmonic progressio...Read More
  • Linear Equations

    A linear equation is that expression in math which when plotted in coordinate system produces a straight line. Equations are not always linear; they can be of several types or geometries. Linear equations can be defined as equ...Read More

  • Solving linear equations in one variable
    When linear equations consist of only one variable, it becomes easier for us to solve the equations. Such kind of equations represent a vertical (perpendicular to x- axis or parallel to y- axis) or horizontal str...Read More
  • Factoring

    Algebra factoring works on basis of factor theorem that can be called as a consequence of remainder theorem. Factor theorem gives factoring definition as follows:

    If q(y) is a polynomial in variable 'y', which when divided by y- b leaves...Read More

  • Systems of Linear Equations

    Linear equation can be defined as an equation which makes a straight line when it is plotted on a graph. Generally linear equation is written in form y = mx + b, Here ‘m’ represents the slope of line and ‘c’ denotes...Read More

  • Introduction to Functions

    Introduction to Functions in mathematics can be given by representation of relationship between a set of variables and constants. These are used to solve equations for unknown variables. A function possesses unique ou...Read More

  • Powers and Roots

    Powers can be defined as process of multiplying a number itself multiple number of times. Powers are also called as indices.

    Suppose 2n in this example n = power, index. If we put n = 2, that means we want to calculate 22 ...Read More

  • Rational Expressions
    When a function is represented by ratio of two polynomials then this function is called as rational expression. In other words a rational expression is a fraction which is comprised of numerator and denominator where numerator and deno...Read More
  • Applications of Linear Equations and Linear Inequalities in One Variable

    Linear inequality is a combination of linear expression and an inequality. An inequality is represented by sign of 'greater than' (>), 'less than' (<), greater than and e...Read More

Math Topics
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