 Hello and welcome to the session. In this session we shall discuss the topic of removal of brackets and redmas. First we discuss the removal of brackets. In this session which involves brackets, we follow certain order of removal of brackets. So let's see what is the order of the removal of brackets. First we remove the bar which is of this kind. Then next we remove the parenthesis which are of this kind. Then next we remove the poorly brackets that is these brackets. And next we remove the square brackets. These are the square brackets. We have to keep pumping in mind which is that when there is a minus sign before a bracket we remove the bracket by changing the sign of the terms inside the bracket. Let's consider one example in which we are supposed to simplify an expression given as minus 2 square bracket open plus 2 bracket open 3P minus 4Q minus 6 parenthesis open 3P minus 2Q minus 6. 2Q minus 6 is under a bar, parenthesis closed, poorly brackets closed and the square bracket closed. That is the expression. Now as you can see this expression involves brackets. So we can simplify this expression by following this order of the removal of brackets. First we need to remove the bar and removing the bar we would get the expression as minus 2 square bracket open P plus Q minus poorly bracket open 3P minus 4Q minus 3P P that 2Q minus 6 is under the bar and there is a minus sign before this. And we have already discussed that when there is a minus sign before a bracket then we remove the bracket by changing the sign of the terms inside the bracket. There is the minus sign before 2Q minus 6 which is under the bar. So when we remove this bar we would change the signs of the terms inside or you can say under this bar. So we would have 3P minus 2Q plus 6 parenthesis closed poorly bracket closed square bracket closed. Now in this expression so obtained we don't have any more bars in this. So next we have to remove the parenthesis. These are the parenthesis as you can see let us now remove these parenthesis. So this would be equal to minus 2 square bracket open P plus Q minus poorly bracket open 3P minus 4Q. Now when we have to remove these parenthesis you can see that we have minus 6 before these parenthesis. So we need to multiply each term inside the parenthesis by minus 6 by 3P would give us minus 18P minus 6 multiplied by minus 2Q would give us plus 12Q minus 6 multiplied by plus 6 would give us minus 36. So this removes our parenthesis then we have poorly bracket closed square bracket closed. Now as you can see in the obtained expression we don't have any more parenthesis. So now next we shall remove the poorly brackets and we need to remove these brackets now. So this is equal to minus 2 square bracket open P plus Q. Now as you can see we have this minus sign before the poorly bracket. So this means when we remove these poorly brackets the signs of the terms inside the poorly brackets would also change. In this 3P only bracket we have plus 3P changed we get minus 3P minus 4Q would become 2 minus 18P would become plus 18P plus 12Q becomes minus 12Q minus 36 becomes plus 36. So this removes our poorly brackets bracket closed and removes the square brackets in expression that is the brackets expression inside the square bracket. So we get this is equal to minus 2 square bracket open now P minus 3P plus 18P gives us 16P then Q plus 4Q minus 12Q gives us minus 7Q plus 36 and square bracket closed. Now as you can see we have minus 2 before the square bracket. So to remove these square brackets we need to multiply each term of the square bracket with minus 2 is equal to minus 2 into 16P which is minus 32P minus 2 into minus 7Q is plus 14Q. Minus 2 into plus 36 is minus 72. Now we don't have any brackets in this obtained expression. So this means we have simplified the given expression to this. An expression involving brackets expressions by solving the order of removal of the brackets. Next let's discuss the board mass rule for solving algebraic expressions which contains various mathematical operations. So we can say that board mass rule algebraic expression, various mathematical operations like plus division, multiplication, multiplication, multiplication. First we consider the brackets. Now let's first we solve the brackets and in the board mass rule which is the letter O of the board mass rule division which is the letter D of the board mass rule. Next is multiplication which is letter M of the board mass rule which is letter A of the board mass rule. Finally we do the subtraction the letter S of the board mass rule. So for the simplification of the algebraic expressions we will follow this order which is the board mass rule. Now consider an example where we need to simplify the algebraic expression given as into 60x divided by parenthesis open 5x plus 2x algebraic expression involves the mathematical operations like expression. We need to follow the board mass rule of the brackets, then of, then division, then multiplication, then addition, then subtraction. First let's look for the brackets. In this algebraic expression we have the parenthesis here. So we need to remove the parenthesis to be equal to divided by. Now removing the parenthesis means which is 5x plus 2x and that is 7x. Now after the brackets are done let's look out for what would be equal to 7x into multiplication. So minus 7x square multiplied by 8x gives us minus x cube divided by 7x. Then after this we do the division. This is the division sign. So we need to divide these two terms. So further we get now minus 56x cube divided by division we do multiplication. So we will multiply these two terms. So this would be equal to 64x square addition we do the addition. But since there is no addition symbol expression so we would not perform any addition. We will move on to the subtraction of these two. Square gives us expression we get 56x square. We are given an expression which involves the mathematical operations. We can easily simplify the algebraic expression using the board mass rule. This completes the session. Hope you understood the concept of removal of brackets and board mass rule.