RD Sharma Solutions (Part - 1) - Ex - 7.2, Algebraic Expressions, Class 7, Math Class 7 Notes | EduRev

RD Sharma Solutions for Class 7 Mathematics

Created by: Abhishek Kapoor

Class 7 : RD Sharma Solutions (Part - 1) - Ex - 7.2, Algebraic Expressions, Class 7, Math Class 7 Notes | EduRev

The document RD Sharma Solutions (Part - 1) - Ex - 7.2, Algebraic Expressions, Class 7, Math Class 7 Notes | EduRev is a part of the Class 7 Course RD Sharma Solutions for Class 7 Mathematics.
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Question 1:

Add the following:
 (i) 3x and 7x
 (ii) −5xy and 9xy

Answer 1:

We have
(i) 3x + 7x = (3 + 7)x = 10x
(ii) -5xy + 9xy = ( -5 + 9)xy = 4xy

Question 2:

Simplify each of the following:
 (i) 7x3y + 9yx3
 (ii) 12a2b + 3ba2

Answer 2:

Simplifying the given expressions, we have
(i) 7x3y + 9yx3 = (7 + 9)x3y = 16x3y
(ii) 12a2b + 3ba2 = (12 + 3)a2b = 15a2b

Question 3:

Add the following:
 (i) 7abc, −5abc, 9abc, −8abc
 (ii) 2x2y, − 4x2y, 6x2y, −5x2y

Answer 3:

Adding the given terms, we have
(i) 7abc + (- 5abc) + (9 abc) + (- 8abc)
    = 7abc - 5abc + 9abc - 8abc
    = (7 - 5 + 9 - 8)abc
    = (16 - 13)abc
    = 3abc

(ii) 2x2y + (- 4x2y) + 6x2y + (- 5x2y)
    = 2x2y - 4x2y + 6x2y - 5x2y
    = (2 - 4 + 6 - 5)x2y
    = (8 - 9)x2y
    = -x2y

 

Question 4:

Add the following expressions:
 (i) x3−2x2y+3xy2−y3, 2x3−5xy2+3x2y−4y3x3-2x2y+3xy2-y3, 2x3-5xy2+3x2y-4y3
 (ii) a4−2a3b+3ab3+4a2b2+3b4,−2a4−5ab3+7a3b−6a2b2+b4a4-2a3b+3ab3+4a2b2+3b4,-2a4-5ab3+7a3b-6a2b2+b4

Answer 4:

Adding the given expressions, we have
(i) x3- 2x2y + 3xy2- y3+ 2x3- 5xy2 + 3x2y- 4y3
     Collecting positive and negative like terms together, we get
     x3+ 2x3- 2x2y + 3x2y + 3xy2- 5xy2 - y3 - 4y3
   = 3x3 + x2y - 2xy2 - 5y3

(ii) (a4- 2a3b + 3ab3 + 4a2b2 + 3b4) + (-2a4- 5ab3 + 7a3b - 6a2b2 + b4)
      a4- 2a3b + 3ab3 + 4a2b2 + 3b4 - 2a4- 5ab3 + 7a3b - 6a2b2 + b4
      Collecting positive and negative like terms together, we get
     a4 - 2a4 - 2a3b + 7a3b + 3ab3 - 5ab3 + 4a2b2 - 6a2b2 + 3b4 + b4
    = - a4 + 5a3b - 2ab3 -  2a2b2 + 4b4

Question 5:

Add the following expressions:
 (i) 8a−6ab+5b, −6a−ab−8b and −4a+2ab+3b8a-6ab+5b, -6a-ab-8b and -4a+2ab+3b
 (ii) 5x3+7+6x−5x2, 2x2−8−9x, 4x−2x2+3x3, 3x3−9x−x2 and x−x2−x3−45x3+7+6x-5x2, 2x2-8-9x, 4x-2x2+3x3, 3x3-9x-x2 and x-x2-x3-4

Answer 5:

(i) Required expression = (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) Required expression = (5x3 + 7 + 6x - 5x2) + (2x2 - 8 - 9x) + (4x - 2x2 + 3x3) + (3x3- 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
    = 11x3 - x3 - 7x2 + 11x - 18x + 7 - 12
    = 10x3 - 7x2 - 7x - 5

Question 6:

Add the following:
 (i)x−3y−2z
 5x+7y−8z
 3x−2y+5z

 (ii)4ab−5bc+7ca
 −3ab+2bc−3ca
 5ab−3bc+4ca

Answer 6:

(i)  Required expression = (x - 3y - 2z) + (5x +7y - 8z) +(3x - 2y + 5z)
     Collecting positive and negative like terms together, we get
     x + 5x + 3x - 3y + 7y - 2y - 2z - 8z + 5z
  = 9x - 5y + 7y - 10z + 5z
  = 9x + 2y - 5z

(ii) Required expression = (4ab - 5bc + 7ca) + (- 3ab + 2bc - 3ca ) + (5ab - 3bc + 4ca)
      Collecting positive and negative like terms together, we get
      4ab - 3ab + 5ab - 5bc + 2bc - 3bc + 7ca - 3ca + 4ca
   = 9ab - 3ab - 8bc + 2bc + 11 ca  - 3ca
   = 6ab - 6bc + 8ca

Question 7:

Add 2x2 − 3x + 1 to the sum of 3x2 − 2x and 3x + 7.

Answer 7:

 Sum of 3x2 - 2x and 3x + 7
= (3x2 - 2x) + ( 3x +7)
= 3x2 - 2x + 3x + 7
= (3x2 + x  + 7)
Now, required expression = (2x2 - 3x + 1) + (3x2 + x  + 7)
                                            = 2x2 + 3x- 3x + x + 1 + 7
                                            = 5x2 - 2x + 8

Question 8:

Add x2 + 2xy + y2 to the sum of x2 − 3y2 and 2x2y2+ 9.

Answer 8:

Sum of x2 - 3y2 and 2x2 - y2 + 9
= (x2 - 3y2) + (2x2 - y2 + 9)
= x2 + 2x2 - 3y2 - y2+ 9
= 3x2 - 4y2 + 9

Now, required expression = (x2 + 2xy + y2) + (3x2 - 4y2 + 9)
                                       = x2 + 3x2 + 2xy + y2 - 4y2 + 9
                                       = 4x2 + 2xy  - 3y2 + 9

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