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Add the following expressions:

(i) 8a – 6ab +5b, –6a – ab – 8b and –4a + 2ab + 3b

(ii) 5x3+ 7 + 6x - 5x2, 2x2 – 8 - 9x, 4x - 2x2 + 3 x 3, 3 x 3 - 9x - x2 and x - x2 - x3 – 4

Answer:

(i) Given 8a – 6ab + 5b, –6a – ab – 8b and –4a + 2ab+ 3b

= (8a – 6ab + 5b) + (–6a – ab – 8b) + (–4a + 2ab + 3b)

Collecting positive and negative like terms together, we get

= 8a – 6a – 4a –6ab – ab + 2ab + 5b – 8b + 3b

= 8a – 10a – 7ab+ 2ab + 8b – 8b

= –2a – 5ab

(ii) Given 5x3 + 7 + 6x - 5x2,

2x2 – 8 - 9x, 4x - 2x2 + 3 x 3, 3 x 3 - 9x - x2 and x - x2 - x3 – 4

= (5 x 3 + 7+ 6x - 5x2) + (2 x 2 – 8 - 9x) + (4x - 2x2+ 3 x 3) + (3 x 3 - 9x-x2) + (x - x2 - x3 - 4)

Collecting positive and negative like terms together, we get

5x3 +3x3 + 3x3 - x3 - 5x2 + 2x2- 2x2- x2 - x2 + 6x - 9x + 4x - 9x + x + 7 – 8- 4

= 10x3- 7x2 - 7x – 5

hello everybody welcome to leader learning channel my name is rachana chaudhary and we are going to add these following algebraic expressions so i already have written these algebraic expressions with plus sign as you all can see here so this is first expression this is second expression this is third expression i have written them with brackets with plus sign already to save the time so let's uh we are going to check the like terms next because all the brackets are with a plus sign outside so we do not need to open the bracket we can check for the like terms as it is because if we will open the bracket we are still going to get the same terms with no change in them so we can check for the like terms as it is here so here let's see 8 a minus 6 a and minus 4 a are the like terms so let's solve them 8 a minus 6 a is 2a and 2 a minus 4 a is minus 2a because we have subtracted them they were of different sign so 4 minus 2 is 2 and a as it is so after subtracting these like terms we have minus 2a let's write that we can check for the next like terms let's see plus 5b minus 8 b and plus 3 b so plus 5 b and plus 3 b is plus 8 b and then we have minus 8 b so they are cancelled out and giving us 0 so then we can write rest of the terms as it is so minus 6 a b and minus a b and plus 2 a b are left and we can again see that all these three are like terms so let's solve them minus six a b and minus a b same sign so we have to add them minus six a b minus a b is minus seven a b and then minus 7 a b plus 2 a b is going to give us that was minus 7 a b and plus 2 a b so it is minus 5 a b so let's write here so minus 2a as it is and we are getting minus 5 a b so this is our final answer we cannot simplify it further so this is the answer for first question let's solve the second one i again have written all the terms with plus sign because we had to add them so we can again check for like terms we can see that 5 x cube and let's check for the cube terms of x so then we have plus 3 x cube then we have plus 3 x cube here and one more x cube so if we will solve them together we can see 5 x cube plus 3 x cube plus 3 x cube are all of plus sign so 5 plus 3 plus 3 is going to give us 11. so 11 x cube so then 11 x cube i'm writing at the bottom 11 x cube minus x cube is 10 x cube so let's write it we have solved the x cube term so that is 10 x cube let's check for the next um like term we can see in the same question let's check for the square term we have minus 5 square then we have plus 2 x square then we have minus 2 x square then we have minus x square and minus x square here so in all these x square terms plus 2x square and minus 2x square would be cancelled out because uh they are same terms with two different signs rest left is i'm writing at the bottom minus 5 5 x square minus x square and minus x square so they all are of same sign so we have to add them so 5 plus 1 plus 1 is 7 x square with minus sign because we have minus all over so answer from from this like term is minus 7 x square then let's see what are the terms which are left we can write them first of all and we can solve them later so plus 7 plus six x minus eight minus nine x plus four x minus nine x plus x and minus 4. now again we can check for the like terms so we can say that plus 7 minus 8 and minus 4 are the like terms they are the constants so we can solve them let's i'm writing at the bottom plus 7 minus 8 minus 4 so we can solve them together for they are of same sign so 7 minus 8 and minus 4 is minus 12 then we can simplify these two and we'll get minus 5 because 12 is a bigger number after ignoring the symbol so we have minus 5 so we can write these two terms because we do not have their like terms as it is so 10 x cubed minus 7 x square as it is and when we have solved these constants we have minus 5 now we are left with plus 6 x i'm circling them plus 6 x minus 9 x plus 4 x minus 9 x and plus x all the x terms so i'm writing at the bottom so we can say that minus term minus term and yeah these are the two minus terms so from here we have minus 18 x and from rest of the plus terms we have 10 and one 11 x then we simplified them this one we have minus 7 x so from the x term we have minus 7 x so this is going to be our answer we can reorganize that in the form like 10 x cube minus 7 x square minus 7 x minus 5 in the descending order of their degrees so this is going to be our answer as we cannot simplify it further because these all are unlike terms so this is the answer for the question i hope you understand the method i'll see in the next video and till then don't forget to like comment and subscribe leader learning channel thank you

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