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RD Sharma Solutions Class 7 Mathematics Solutions for Algebraic Expressions Exercise 7.2 in Chapter 7 - Algebraic Expressions

Question 17 Algebraic Expressions Exercise 7.2
  1. From the sum of x2 + 3y2 − 6xy, 2x2 − y2 + 8xy, y2 + 8 and x2 − 3xy subtract−3x2 + 4y2– xy + x – y + 3.
Answer:

First we have to find the sum of (x2 + 3y2- 6xy), (2x2 - y2 + 8xy), (y2 + 8) and (x2- 3xy)

={(x2 + 3y2 - 6xy) + (2x2 - y2+ 8xy) + ( y2 + 8) + (x2 - 3xy)}

={x2 + 3y2 - 6xy + 2x2 - y2+ 8xy + y2 + 8 + x2 - 3xy}

= {x2+ 2x2+ x2 + 3y2-y2 + y2- 6xy + 8xy - 3xy + 8}

= 4x2 + 3y2 - xy + 8

Now, from the result subtract the −3x2 + 4y2 –xy + x – y + 3.

Therefore, required expression = (4x2 + 3y2 -xy + 8) - (- 3x2 + 4y2 - xy + x - y + 3)

= 4x2 + 3y2 - xy + 8 + 3x2- 4y2 + xy - x + y - 3

= 4x2 + 3x2+ 3y2- 4y2- x+ y - 3 + 8

= 7x2 - y2- x + y + 5

Video transcript
hello everybody welcome to leader learning my name is rachna chaudhary and we are we are going to solve this question we can see in this question it is written from the sum of then there are four expressions we have to subtract another expression so we have to find the sum of four expressions then we have to subtract another expression from it so i have already written uh all those four expressions with plus sign so because we do not need to open the bracket we are only adding them if uh there have been minus sign at these places then we need to open the bracket but we are not going to do that in this let's move ahead by finding the like terms so we can see that x square 2 x square and this x square are like terms here so x square plus 2x square plus x square is going to be 4 x square because these all are the like terms then let's see the next like terms then let's see uh that plus 3y square plus minus y square and this plus y square so um y plus y square and minus y square we can cancel them because we have two same terms with two different uh symbols so we can cancel them and we are left with plus three y square so let's write plus 3 by square let's see next like terms so we can see here we have minus 6 x y plus 8 x y and minus 3 x y so i'm writing them here minus 6 x y plus 8 x y minus 3 x y so we can see that that these are two uh like terms with two same sign so we have to add them we'll get minus nine x y then we have to subtract plus eight x y from it so we'll get minus x y because minus 9 plus 8 is 1 so 1 x y we can write as just x y so from these terms we have minus x y let's write that then we are left with one more term that is plus 8 because that is a constant and we do not have any other constant to solve it with so we can write it as it is plus 8 so this is the sum now we have to subtract another expression from this sum so i'm writing the sum here so 4x square plus 3y square minus xy plus 8 now we have to subtract another expression so i'll write that in bracket with the minus sign now we are going to open the bracket and all the terms will become of their opposite sign minus 3x square minus 4y square plus xy minus x plus y minus 3. now we are going to find again the like terms so here we can see uh that uh 4x square and minus 3x square are the like terms so 4x square minus 3x square is going to be x square 4 minus 3 is 1 that means just x square so let's write that next we have 3y square and minus 4y square so 3y square minus 4y square is minus y square next we have minus xy and plus xy so they would be cancelled out then we are left with minus x and plus y here because these are two unlike terms there is no other term so that we can solve with them we can write minus x and plus y as it is then we can say we have two more terms uh plus eight and minus three so plus 8 and minus 3 are going to be plus 5 so this is our final answer we cannot solve it further because these all are unlike terms so this is all from my side i hope you understand the method okay i would like to add one more thing here we can see that in the question we have uh we have to subtract minus 3 x square and in the question we have written a plus 3 x square here so i would like to correct this here is minus so this minus 3x square would become plus 3x square because we are opening the bracket here now because this is uh plus 3x square and we have to solve this as 4 x square so it would be plus 7 x square so i'm going to correct that so this is plus 7 x squared so this is all for the question don't forget to like comment and subscribe leader learning channel thank you
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