 Hi and welcome to the session. Today we will learn how to find the value of an expression. Consider the expression 4x squared plus 2xy minus 3. Suppose we want to find the value of the given expression for x equal to 2 and y equal to 3. Then for these values of x and y 4x squared plus 2xy minus 3 will be equal to 4 into 2 squared as the value of x is 2 plus 2 into x that is 2 into y that is 3 minus 3. So this is equal to 16 plus 12 minus 3 which is equal to 25. Thus the value of the given expression for x equal to 2 and y equal to 3 is 25. Now let's see how we can use algebraic expressions for formulas on rules. First of all let's see the use of algebraic expressions for formulas. Consider a rectangle. We know the perimeter of a rectangle is equal to 2 into length plus breadth. Now if we denote the length of the rectangle by n and breadth of the rectangle by v then perimeter will be given by 2 into n plus v which is an algebraic expression. Similarly area of the rectangle is equal to length into breadth. Now as length is denoted by l and breadth is denoted by v so area will be given by the algebraic expression l into v that is l v. Now suppose we want to find the perimeter of a rectangle whose length is given to be 5 centimeters and width is given to be 3 centimeters. Now we know that perimeter of the rectangle is equal to 2 into l plus v then l denotes the length and v denotes the breadth of the rectangle. So let's substitute the values of l and v so this will be equal to 2 into l that is 5 plus v that is 3 centimeters which is equal to 16 centimeters. Now let's see how we can use algebraic expressions in rules for number patterns. Suppose we denote a natural number by n then its successor will be given by n plus 1 which is an algebraic expression. Let us take the value of n equal to 21 so successor 21 will be n plus 1 that is 21 plus 1 equal to 22. So that means the algebraic expression n plus 1 gives the successor of a natural number n. Now again suppose we denote a natural number by n then 2n will be an even number 2n plus 1 will be an odd number for any value of n. Here also let us take the value of n equal to 21 so 2n will be equal to 2 into 21 that is 42 and we know that 42 is an even number plus 1 will be equal to 2 into 21 plus 1 which will be equal to 43 and 43 is an odd number. Let us see one more number pattern let us take the multiples of 5 and arrange them in increasing order so first of all we will have 5 then 10 15 20 25 and so on. So here the term at first position is 5 into 1 the term at second position is 5 into 2 term at third position is 5 into 3 term at fourth position is 5 into 4 and so on that means the term at nth position will be 5 into n that is 5n. So let us find out the multiple of 5 at 15th position that will be 5 into 15 which will be equal to 75. Similarly if we find the multiple of n at 100th position then that will be given by 5 into 100 which is equal to 500. And now let us see one pattern in geometry let us see the number of diagonals we can draw from one vertex of a polygon first of all let us take a polygon with 4 sides that is a quadrilateral. So here we have a quadrilateral a v c d now let us see how many diagonals we can draw from one vertex that is vertex a of this quadrilateral. In this we can draw only one diagonal now let us take a polygon with 5 sides that is a pentagon in a pentagon we can draw 2 diagonals from a vertex. Now we have a polygon with 6 sides that is hexagon in a hexagon we can draw 3 diagonals from a vertex. Now let us see the pattern in this here in a polygon with 4 sides we can draw 1 diagonal that is 4 minus 3. Now in a polygon with 5 sides we can draw 2 diagonals that is 5 minus 3. In a polygon with 6 sides we can draw 3 that is 6 minus 3 sides and so on. So in a polygon with n sides we can draw n minus 3 diagonals. So if we want to find out the number of diagonals we can draw in a polygon with 8 sides that is a octagon. So this will be equal to 8 minus 3 that is 5 diagonals. With this we finished this session hope you must have enjoyed it goodbye take care and keep smiling.