 Hi and welcome to the session. Today we will learn about algebraic expressions. Let us learn how expressions are formed. So for that first of all let us see what is a constant and what is a variable. Constant is a symbol having fixed numerical value for example say 21 minus 5 etc. Now variable is a symbol various numerical values. The value of a variable is not fixed. Now variables are denoted by letters such as A, B, C, X, Y, P etc. Now let us see how algebraic expressions are formed. Algebraic expressions are formed by the combination of constants and variables did by some or all of the four fundamental operations that is addition, subtraction, multiplication and division. Let us take an example. First of all let us combine the constant for variable X and X by multiplication. So we get 4X squared. Now we will combine minus 7X and Y by multiplication. So this will give us minus 7X, Y and lastly let us take a constant that is 11 and now we will combine all these three parts by addition. So we get 4X squared plus minus 7X, Y plus 11 which can also be written as 4X squared minus 7X, Y plus 11. So this is an algebraic expression but one thing that you must keep in mind that all these three parts separately are also algebraic expressions. Now let us see what are the terms of an algebraic expression. Let us consider this algebraic expression that is 4X squared minus 7X, Y plus 11. Here we got this algebraic expression by adding three parts that is 4X squared minus 7X, Y and 11. So here all these three parts are the three terms of the given algebraic expression. Now here we cannot say that 7X, Y is a term of this algebraic expression because the sign along with the part is known as a term. So minus 7X, Y is the term of this algebraic expression. Now let us move on to factors of a term of algebraic expression. Again we will consider the same algebraic expression that is 4X squared minus 7X, Y plus 11. Here the terms of this algebraic expression are 4X squared minus 7X, Y and 11. See the factors of that will be 4X and X because we got 4X squared by multiplying 4X and X. So these three are the factors of the term 4X squared. Similarly the factors of minus 7X, Y will be minus 7X and Y. Now 11 is a constant term because there are no literal factors along with it that is there are no variables. So 11 is the only factor of this term. Next let us see the coefficients of a term. Let us consider the same algebraic expression 4X squared minus 7X, Y plus 11. Here for the first term that is 4X squared let us find the coefficient of this term. The factors of this term are 4X and X. Now 4 is the numerical factor of this term. So the numerical factor of the given term is known as the numerical coefficient of the term or simply coefficient of the term. Now the coefficient of the term minus 7X, Y will be minus 7. Now if we have a term say XY then the coefficient of this term will be 1 as XY can be written as 1 into XY. So 1 is the numerical factor of this term. Similarly if we have a term minus X squared then X coefficient will be minus 1 because we can write minus X squared as minus 1 into X squared. So here minus 1 is the numerical factor of the given term. Let us consider a term 4X squared Y. Here 4 is the coefficient of the term and we can also say that 4 is the coefficient of X squared Y. That is the coefficient of the remaining factors. Similarly if we want to find out the coefficient of 4X squared then that will be Y. If I want to find out the coefficient 4Y then that will be equal to X squared. That means we can say that a coefficient can be a numerical factor or an algebraic factor or maybe the product of two or more factors. Now let us see what are like and unlike terms. Like terms are the terms which have seen algebraic factors and unlike terms are the terms which have different algebraic factors. Let us take an example. Suppose we have an algebraic expression 3PQ plus 5P minus 11PQ minus 4. Here in first term the algebraic factors that is the variable factors are P and Q. In second term the algebraic factor is P. In third term the algebraic factors are P and Q and in fourth term there is no algebraic factor. So here the first term and third term that is 3PQ and minus 11PQ have same algebraic factors that is P and Q. So that means 3PQ and minus 11PQ are like terms. Now let us see the unlike terms. Here 3PQ and 5P have different algebraic factors so that means 3PQ and 5P are unlike terms. Similarly 3PQ and minus 4 are unlike terms. Also 5P and minus 4 are unlike terms. So in this way we can find out like terms and unlike terms in a given algebraic expression. Now let us see what are monomials, binomials, binomials and polynomials. An expression with only one term is known as a monomial. For example fx squared minus 6a 11 etc are all monomials. Now expression with two unlike terms is called a binomial. For example 3a plus 5vc 21x squared y plus 30xy squared P plus Q etc are all binomials. Next we have expression with three unlike terms is called a trinomial. For example 5x squared plus 2x plus 1 a plus b plus c etc are trinomials. Lastly we have polynomials. An expression with one or more is called a polynomial. That means polynomial is a general term used for algebraic expression. Here monomials, binomials and trinomials are all included in polynomials. So the examples of monomials, binomials and trinomials can be considered as the examples of polynomials. With this we finish this session. Hope you must have understood all the concepts. We are buying take care and have a nice day.