RD Sharma Solutions (Part - 1) - Ex - 7.2, Algebraic Expressions, Class 7, Math | RD Sharma Solutions for Class 7 Mathematics PDF Download

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 + 3x² - 3x + x + 1 + 7
                                            = 5x² - 2x + 8

Question 8:

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