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Class 7 Exam  >  Class 7 Notes  >  Mathematics (Maths) Class 7  >  RD Sharma Solutions: Algebraic Expressions (Exercise 7.2)

Algebraic Expressions (Exercise 7.2) RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download

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 Page 1


 
 
 
 
 
 
 
Exercise 7.2         Page No: 7.13 
 
1. Add the following: 
(i) 3x and 7x 
(ii) -5xy and 9xy 
 
Solution: 
(i) Given 3x and 7x 
3x + 7x = (3 + 7) x  
= 10x 
 
(ii) Given -5xy and 9xy 
-5xy + 9xy = (-5 + 9) xy  
= 4xy 
 
2. Simplify each of the following: 
(i) 7x
3
y +9yx
3
 
(ii) 12a
2
b + 3ba
2
 
 
Solution: 
(i) Given 7x
3
y +9yx
3
 
7x
3
y + 9yx
3
 = (7 + 9) x
3
y  
= 16x
3
y 
 
(ii) Given  
12a
2
b + 3ba
2 
= (12 + 3) a
2
b  
= 15a
2
b 
 
3. Add the following: 
(i) 7abc, -5abc, 9abc, -8abc 
(ii) 2x
2
y, - 4x
2
y, 6x
2
y, -5x
2
y 
 
Solution: 
(i) Given 7abc, -5abc, 9abc, -8abc 
Consider 7abc + (-5abc) + (9abc) + (-8abc) 
= 7abc – 5abc + 9abc – 8abc 
Page 2


 
 
 
 
 
 
 
Exercise 7.2         Page No: 7.13 
 
1. Add the following: 
(i) 3x and 7x 
(ii) -5xy and 9xy 
 
Solution: 
(i) Given 3x and 7x 
3x + 7x = (3 + 7) x  
= 10x 
 
(ii) Given -5xy and 9xy 
-5xy + 9xy = (-5 + 9) xy  
= 4xy 
 
2. Simplify each of the following: 
(i) 7x
3
y +9yx
3
 
(ii) 12a
2
b + 3ba
2
 
 
Solution: 
(i) Given 7x
3
y +9yx
3
 
7x
3
y + 9yx
3
 = (7 + 9) x
3
y  
= 16x
3
y 
 
(ii) Given  
12a
2
b + 3ba
2 
= (12 + 3) a
2
b  
= 15a
2
b 
 
3. Add the following: 
(i) 7abc, -5abc, 9abc, -8abc 
(ii) 2x
2
y, - 4x
2
y, 6x
2
y, -5x
2
y 
 
Solution: 
(i) Given 7abc, -5abc, 9abc, -8abc 
Consider 7abc + (-5abc) + (9abc) + (-8abc) 
= 7abc – 5abc + 9abc – 8abc 
 
 
= (7 – 5 + 9 – 8) abc [by taking abc common] 
= (16 – 13) abc 
= 3abc 
(ii) Given 2x
2
y, - 4x
2
y, 6x
2
y, -5x
2
y
2x
2
y +(-4x
2
y) + (6x
2
y) + (-5x
2
y)
= 2x
2
y - 4x
2
y + 6x
2
y - 5x
2
y
= (2- 4 + 6 - 5) x
2
y [by taking x
2
 y common]
= (8 - 9) x
2
y
= -x
2
y
4. Add the following expressions:
(i) x
3
 -2x
2
y + 3xy
2
- y
3
, 2x
3
- 5xy
2
 + 3x
2
y - 4y
3
(ii) a
4
 - 2a
3
b + 3ab
3
 + 4a
2
b
2 
+ 3b
4
, - 2a
4
 - 5ab
3
 + 7a
3
b - 6a
2
b
2 
+ b
4
Solution: 
(i) Given x
3
 -2x
2
y + 3xy
2
- y
3
, 2x
3
- 5xy
2
 + 3x
2
y - 4y
3
Collecting positive and negative like terms together, we get
= x
3
 +2x
3 
- 2x
2
y + 3x
2
y + 3xy
2
 - 5xy
2
 - y
3
- 4y
3
= 3x
3
 + x
2
y - 2xy
2 
- 5y
3
(ii) Given a
4
 - 2a
3
b + 3ab
3
 + 4a
2
b
2 
+ 3b
4
, - 2a
4
 - 5ab
3
 + 7a
3
b - 6a
2
b
2 
+ b
4
= a
4
 - 2a
3
b + 3ab
3
 + 4a
2
b
2
 + 3b
4
 - 2a
4
 - 5ab
3 
+ 7a
3
b - 6a
2
b
2
 + b
4
Collecting positive and negative like terms together, we get
= a
4
 - 2a
4
- 2a
3
b + 7a
3
b + 3ab
3
 - 5ab
3
 + 4a
2
b
2
 - 6a
2
b
2 
+ 3b
4
 + b
4
= - a
4 
+ 5a
3
b - 2ab
3
 - 2a
2
b
2 
+ 4b
4
5. Add the following expressions:
(i) 8a – 6ab + 5b, –6a – ab – 8b and –4a + 2ab + 3b
(ii) 5x
3
 + 7 + 6x - 5x
2
, 2x
2
 – 8 - 9x, 4x - 2x
2
 + 3 x 3, 3 x 3 - 9x - x
2
 and x - x
2
 - x
3
 – 4
Solution: 
(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
Page 3


 
 
 
 
 
 
 
Exercise 7.2         Page No: 7.13 
 
1. Add the following: 
(i) 3x and 7x 
(ii) -5xy and 9xy 
 
Solution: 
(i) Given 3x and 7x 
3x + 7x = (3 + 7) x  
= 10x 
 
(ii) Given -5xy and 9xy 
-5xy + 9xy = (-5 + 9) xy  
= 4xy 
 
2. Simplify each of the following: 
(i) 7x
3
y +9yx
3
 
(ii) 12a
2
b + 3ba
2
 
 
Solution: 
(i) Given 7x
3
y +9yx
3
 
7x
3
y + 9yx
3
 = (7 + 9) x
3
y  
= 16x
3
y 
 
(ii) Given  
12a
2
b + 3ba
2 
= (12 + 3) a
2
b  
= 15a
2
b 
 
3. Add the following: 
(i) 7abc, -5abc, 9abc, -8abc 
(ii) 2x
2
y, - 4x
2
y, 6x
2
y, -5x
2
y 
 
Solution: 
(i) Given 7abc, -5abc, 9abc, -8abc 
Consider 7abc + (-5abc) + (9abc) + (-8abc) 
= 7abc – 5abc + 9abc – 8abc 
 
 
= (7 – 5 + 9 – 8) abc [by taking abc common] 
= (16 – 13) abc 
= 3abc 
(ii) Given 2x
2
y, - 4x
2
y, 6x
2
y, -5x
2
y
2x
2
y +(-4x
2
y) + (6x
2
y) + (-5x
2
y)
= 2x
2
y - 4x
2
y + 6x
2
y - 5x
2
y
= (2- 4 + 6 - 5) x
2
y [by taking x
2
 y common]
= (8 - 9) x
2
y
= -x
2
y
4. Add the following expressions:
(i) x
3
 -2x
2
y + 3xy
2
- y
3
, 2x
3
- 5xy
2
 + 3x
2
y - 4y
3
(ii) a
4
 - 2a
3
b + 3ab
3
 + 4a
2
b
2 
+ 3b
4
, - 2a
4
 - 5ab
3
 + 7a
3
b - 6a
2
b
2 
+ b
4
Solution: 
(i) Given x
3
 -2x
2
y + 3xy
2
- y
3
, 2x
3
- 5xy
2
 + 3x
2
y - 4y
3
Collecting positive and negative like terms together, we get
= x
3
 +2x
3 
- 2x
2
y + 3x
2
y + 3xy
2
 - 5xy
2
 - y
3
- 4y
3
= 3x
3
 + x
2
y - 2xy
2 
- 5y
3
(ii) Given a
4
 - 2a
3
b + 3ab
3
 + 4a
2
b
2 
+ 3b
4
, - 2a
4
 - 5ab
3
 + 7a
3
b - 6a
2
b
2 
+ b
4
= a
4
 - 2a
3
b + 3ab
3
 + 4a
2
b
2
 + 3b
4
 - 2a
4
 - 5ab
3 
+ 7a
3
b - 6a
2
b
2
 + b
4
Collecting positive and negative like terms together, we get
= a
4
 - 2a
4
- 2a
3
b + 7a
3
b + 3ab
3
 - 5ab
3
 + 4a
2
b
2
 - 6a
2
b
2 
+ 3b
4
 + b
4
= - a
4 
+ 5a
3
b - 2ab
3
 - 2a
2
b
2 
+ 4b
4
5. Add the following expressions:
(i) 8a – 6ab + 5b, –6a – ab – 8b and –4a + 2ab + 3b
(ii) 5x
3
 + 7 + 6x - 5x
2
, 2x
2
 – 8 - 9x, 4x - 2x
2
 + 3 x 3, 3 x 3 - 9x - x
2
 and x - x
2
 - x
3
 – 4
Solution: 
(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 5x
3
 + 7 + 6x - 5x
2
, 2x
2
 – 8 - 9x, 4x - 2x
2
 + 3 x
3
, 3 x
3
 - 9x - x
2
 and x - x
2
 - x
3
 – 4 = 
(5 x
3
 + 7+ 6x - 5x
2
) + (2 x
2
 – 8 - 9x) + (4x - 2x
2
 + 3 x
3
) + (3 x
3
 - 9x-x
2
) + (x - x
2
 - x
3
 - 4) 
Collecting positive and negative like terms together, we get
5x
3
 + 3x
3
 + 3x
3
 - x
3
 - 5x
2
 + 2x
2 
- 2x
2
- x
2
 - x
2
 + 6x - 9x + 4x - 9x + x + 7 – 8 - 4
= 10x
3
 - 7x
2
 - 7x – 5
6. Add the following:
(i) x – 3y – 2z
5x + 7y – 8z
3x – 2y + 5z
(ii) 4ab – 5bc + 7ca
–3ab + 2bc – 3ca
5ab – 3bc + 4ca
Solution: 
(i) Given x – 3y – 2z, 5x + 7y – 8z and 3x – 2y + 5z
= (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) Given 4ab – 5bc + 7ca, –3ab + 2bc – 3ca and 5ab – 3bc + 4ca
= (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 + 11ca – 3ca
= 6ab – 6bc + 8ca
7. Add 2x
2
 - 3x + 1 to the sum of 3x
2
 - 2x and 3x + 7.
Solution: 
Given 2x
2
 - 3x + 1, 3x
2
 - 2x and 3x + 7  
sum of 3x
2
 - 2x and 3x + 7 
= (3x
2
 - 2x) + (3x +7) 
Page 4


 
 
 
 
 
 
 
Exercise 7.2         Page No: 7.13 
 
1. Add the following: 
(i) 3x and 7x 
(ii) -5xy and 9xy 
 
Solution: 
(i) Given 3x and 7x 
3x + 7x = (3 + 7) x  
= 10x 
 
(ii) Given -5xy and 9xy 
-5xy + 9xy = (-5 + 9) xy  
= 4xy 
 
2. Simplify each of the following: 
(i) 7x
3
y +9yx
3
 
(ii) 12a
2
b + 3ba
2
 
 
Solution: 
(i) Given 7x
3
y +9yx
3
 
7x
3
y + 9yx
3
 = (7 + 9) x
3
y  
= 16x
3
y 
 
(ii) Given  
12a
2
b + 3ba
2 
= (12 + 3) a
2
b  
= 15a
2
b 
 
3. Add the following: 
(i) 7abc, -5abc, 9abc, -8abc 
(ii) 2x
2
y, - 4x
2
y, 6x
2
y, -5x
2
y 
 
Solution: 
(i) Given 7abc, -5abc, 9abc, -8abc 
Consider 7abc + (-5abc) + (9abc) + (-8abc) 
= 7abc – 5abc + 9abc – 8abc 
 
 
= (7 – 5 + 9 – 8) abc [by taking abc common] 
= (16 – 13) abc 
= 3abc 
(ii) Given 2x
2
y, - 4x
2
y, 6x
2
y, -5x
2
y
2x
2
y +(-4x
2
y) + (6x
2
y) + (-5x
2
y)
= 2x
2
y - 4x
2
y + 6x
2
y - 5x
2
y
= (2- 4 + 6 - 5) x
2
y [by taking x
2
 y common]
= (8 - 9) x
2
y
= -x
2
y
4. Add the following expressions:
(i) x
3
 -2x
2
y + 3xy
2
- y
3
, 2x
3
- 5xy
2
 + 3x
2
y - 4y
3
(ii) a
4
 - 2a
3
b + 3ab
3
 + 4a
2
b
2 
+ 3b
4
, - 2a
4
 - 5ab
3
 + 7a
3
b - 6a
2
b
2 
+ b
4
Solution: 
(i) Given x
3
 -2x
2
y + 3xy
2
- y
3
, 2x
3
- 5xy
2
 + 3x
2
y - 4y
3
Collecting positive and negative like terms together, we get
= x
3
 +2x
3 
- 2x
2
y + 3x
2
y + 3xy
2
 - 5xy
2
 - y
3
- 4y
3
= 3x
3
 + x
2
y - 2xy
2 
- 5y
3
(ii) Given a
4
 - 2a
3
b + 3ab
3
 + 4a
2
b
2 
+ 3b
4
, - 2a
4
 - 5ab
3
 + 7a
3
b - 6a
2
b
2 
+ b
4
= a
4
 - 2a
3
b + 3ab
3
 + 4a
2
b
2
 + 3b
4
 - 2a
4
 - 5ab
3 
+ 7a
3
b - 6a
2
b
2
 + b
4
Collecting positive and negative like terms together, we get
= a
4
 - 2a
4
- 2a
3
b + 7a
3
b + 3ab
3
 - 5ab
3
 + 4a
2
b
2
 - 6a
2
b
2 
+ 3b
4
 + b
4
= - a
4 
+ 5a
3
b - 2ab
3
 - 2a
2
b
2 
+ 4b
4
5. Add the following expressions:
(i) 8a – 6ab + 5b, –6a – ab – 8b and –4a + 2ab + 3b
(ii) 5x
3
 + 7 + 6x - 5x
2
, 2x
2
 – 8 - 9x, 4x - 2x
2
 + 3 x 3, 3 x 3 - 9x - x
2
 and x - x
2
 - x
3
 – 4
Solution: 
(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 5x
3
 + 7 + 6x - 5x
2
, 2x
2
 – 8 - 9x, 4x - 2x
2
 + 3 x
3
, 3 x
3
 - 9x - x
2
 and x - x
2
 - x
3
 – 4 = 
(5 x
3
 + 7+ 6x - 5x
2
) + (2 x
2
 – 8 - 9x) + (4x - 2x
2
 + 3 x
3
) + (3 x
3
 - 9x-x
2
) + (x - x
2
 - x
3
 - 4) 
Collecting positive and negative like terms together, we get
5x
3
 + 3x
3
 + 3x
3
 - x
3
 - 5x
2
 + 2x
2 
- 2x
2
- x
2
 - x
2
 + 6x - 9x + 4x - 9x + x + 7 – 8 - 4
= 10x
3
 - 7x
2
 - 7x – 5
6. Add the following:
(i) x – 3y – 2z
5x + 7y – 8z
3x – 2y + 5z
(ii) 4ab – 5bc + 7ca
–3ab + 2bc – 3ca
5ab – 3bc + 4ca
Solution: 
(i) Given x – 3y – 2z, 5x + 7y – 8z and 3x – 2y + 5z
= (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) Given 4ab – 5bc + 7ca, –3ab + 2bc – 3ca and 5ab – 3bc + 4ca
= (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 + 11ca – 3ca
= 6ab – 6bc + 8ca
7. Add 2x
2
 - 3x + 1 to the sum of 3x
2
 - 2x and 3x + 7.
Solution: 
Given 2x
2
 - 3x + 1, 3x
2
 - 2x and 3x + 7  
sum of 3x
2
 - 2x and 3x + 7 
= (3x
2
 - 2x) + (3x +7) 
 
 
 
 
 
 
 
=3x
2
 - 2x + 3x + 7 
= (3x
2
 + x + 7) 
Now, required expression = 2x
2 
- 3x + 1+ (3x
2 
+ x + 7) 
= 2x
2 
+ 3x
2
 - 3x + x + 1 + 7 
= 5x
2 
- 2x + 8 
 
8. Add x
2 
+ 2xy + y
2
 to the sum of x
2
 - 3y
2
and 2x
2 
- y
2
 + 9. 
 
Solution: 
Given x
2 
+ 2xy + y
2
, x
2
 - 3y
2
and 2x
2 
- y
2
 + 9. 
First we have to find the sum of x
2
 - 3y
2
 and 2x
2
 - y
2
 + 9 
= (x
2
 - 3y
2
) + (2x
2
 - y
2
 + 9) 
= x
2
 + 2x
2
 - 3y
2
 - y
2
+ 9 
= 3x
2
 - 4y
2
 + 9 
Now, required expression = (x
2
 + 2xy + y
2
) + (3x
2
 - 4y
2
 + 9) 
= x
2
 + 3x
2
 + 2xy + y
2
 - 4y
2
 + 9 
= 4x
2
 + 2xy  - 3y
2
+ 9 
 
9. Add a
3
+ b
3
 - 3 to the sum of 2a
3
 - 3b
3 
- 3ab + 7 and -a
3
 + b
3
 + 3ab - 9. 
 
Solution: 
Given a
3
+ b
3
 – 3, 2a
3
 - 3b
3 
- 3ab + 7 and -a
3
 + b
3
 + 3ab - 9. 
First, we need to find the sum of 2a
3
 - 3b
3
- 3ab + 7 and - a
3
 + b
3
 + 3ab - 9. 
= (2a
3
 - 3b
3
- 3ab + 7) + (- a
3
 + b
3
 + 3ab - 9) 
Collecting positive and negative like terms together, we get 
= 2a
3
 - a
3
- 3b
3
+ b
3
 - 3ab + 3ab + 7 - 9 
= a
3
 - 2b
3
 - 2 
Now, the required expression = (a
3
 + b
3
 - 3) + (a
3
 - 2b
3
 - 2). 
= a
3
+ a
3
+ b
3
- 2b
3
 - 3 - 2 
= 2a
3
 - b
3
 - 5 
 
10. Subtract: 
(i) 7a
2
b from 3a
2
b 
(ii) 4xy from -3xy 
 
Solution: 
(i) Given 7a
2
b from 3a
2
b 
Page 5


 
 
 
 
 
 
 
Exercise 7.2         Page No: 7.13 
 
1. Add the following: 
(i) 3x and 7x 
(ii) -5xy and 9xy 
 
Solution: 
(i) Given 3x and 7x 
3x + 7x = (3 + 7) x  
= 10x 
 
(ii) Given -5xy and 9xy 
-5xy + 9xy = (-5 + 9) xy  
= 4xy 
 
2. Simplify each of the following: 
(i) 7x
3
y +9yx
3
 
(ii) 12a
2
b + 3ba
2
 
 
Solution: 
(i) Given 7x
3
y +9yx
3
 
7x
3
y + 9yx
3
 = (7 + 9) x
3
y  
= 16x
3
y 
 
(ii) Given  
12a
2
b + 3ba
2 
= (12 + 3) a
2
b  
= 15a
2
b 
 
3. Add the following: 
(i) 7abc, -5abc, 9abc, -8abc 
(ii) 2x
2
y, - 4x
2
y, 6x
2
y, -5x
2
y 
 
Solution: 
(i) Given 7abc, -5abc, 9abc, -8abc 
Consider 7abc + (-5abc) + (9abc) + (-8abc) 
= 7abc – 5abc + 9abc – 8abc 
 
 
= (7 – 5 + 9 – 8) abc [by taking abc common] 
= (16 – 13) abc 
= 3abc 
(ii) Given 2x
2
y, - 4x
2
y, 6x
2
y, -5x
2
y
2x
2
y +(-4x
2
y) + (6x
2
y) + (-5x
2
y)
= 2x
2
y - 4x
2
y + 6x
2
y - 5x
2
y
= (2- 4 + 6 - 5) x
2
y [by taking x
2
 y common]
= (8 - 9) x
2
y
= -x
2
y
4. Add the following expressions:
(i) x
3
 -2x
2
y + 3xy
2
- y
3
, 2x
3
- 5xy
2
 + 3x
2
y - 4y
3
(ii) a
4
 - 2a
3
b + 3ab
3
 + 4a
2
b
2 
+ 3b
4
, - 2a
4
 - 5ab
3
 + 7a
3
b - 6a
2
b
2 
+ b
4
Solution: 
(i) Given x
3
 -2x
2
y + 3xy
2
- y
3
, 2x
3
- 5xy
2
 + 3x
2
y - 4y
3
Collecting positive and negative like terms together, we get
= x
3
 +2x
3 
- 2x
2
y + 3x
2
y + 3xy
2
 - 5xy
2
 - y
3
- 4y
3
= 3x
3
 + x
2
y - 2xy
2 
- 5y
3
(ii) Given a
4
 - 2a
3
b + 3ab
3
 + 4a
2
b
2 
+ 3b
4
, - 2a
4
 - 5ab
3
 + 7a
3
b - 6a
2
b
2 
+ b
4
= a
4
 - 2a
3
b + 3ab
3
 + 4a
2
b
2
 + 3b
4
 - 2a
4
 - 5ab
3 
+ 7a
3
b - 6a
2
b
2
 + b
4
Collecting positive and negative like terms together, we get
= a
4
 - 2a
4
- 2a
3
b + 7a
3
b + 3ab
3
 - 5ab
3
 + 4a
2
b
2
 - 6a
2
b
2 
+ 3b
4
 + b
4
= - a
4 
+ 5a
3
b - 2ab
3
 - 2a
2
b
2 
+ 4b
4
5. Add the following expressions:
(i) 8a – 6ab + 5b, –6a – ab – 8b and –4a + 2ab + 3b
(ii) 5x
3
 + 7 + 6x - 5x
2
, 2x
2
 – 8 - 9x, 4x - 2x
2
 + 3 x 3, 3 x 3 - 9x - x
2
 and x - x
2
 - x
3
 – 4
Solution: 
(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 5x
3
 + 7 + 6x - 5x
2
, 2x
2
 – 8 - 9x, 4x - 2x
2
 + 3 x
3
, 3 x
3
 - 9x - x
2
 and x - x
2
 - x
3
 – 4 = 
(5 x
3
 + 7+ 6x - 5x
2
) + (2 x
2
 – 8 - 9x) + (4x - 2x
2
 + 3 x
3
) + (3 x
3
 - 9x-x
2
) + (x - x
2
 - x
3
 - 4) 
Collecting positive and negative like terms together, we get
5x
3
 + 3x
3
 + 3x
3
 - x
3
 - 5x
2
 + 2x
2 
- 2x
2
- x
2
 - x
2
 + 6x - 9x + 4x - 9x + x + 7 – 8 - 4
= 10x
3
 - 7x
2
 - 7x – 5
6. Add the following:
(i) x – 3y – 2z
5x + 7y – 8z
3x – 2y + 5z
(ii) 4ab – 5bc + 7ca
–3ab + 2bc – 3ca
5ab – 3bc + 4ca
Solution: 
(i) Given x – 3y – 2z, 5x + 7y – 8z and 3x – 2y + 5z
= (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) Given 4ab – 5bc + 7ca, –3ab + 2bc – 3ca and 5ab – 3bc + 4ca
= (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 + 11ca – 3ca
= 6ab – 6bc + 8ca
7. Add 2x
2
 - 3x + 1 to the sum of 3x
2
 - 2x and 3x + 7.
Solution: 
Given 2x
2
 - 3x + 1, 3x
2
 - 2x and 3x + 7  
sum of 3x
2
 - 2x and 3x + 7 
= (3x
2
 - 2x) + (3x +7) 
 
 
 
 
 
 
 
=3x
2
 - 2x + 3x + 7 
= (3x
2
 + x + 7) 
Now, required expression = 2x
2 
- 3x + 1+ (3x
2 
+ x + 7) 
= 2x
2 
+ 3x
2
 - 3x + x + 1 + 7 
= 5x
2 
- 2x + 8 
 
8. Add x
2 
+ 2xy + y
2
 to the sum of x
2
 - 3y
2
and 2x
2 
- y
2
 + 9. 
 
Solution: 
Given x
2 
+ 2xy + y
2
, x
2
 - 3y
2
and 2x
2 
- y
2
 + 9. 
First we have to find the sum of x
2
 - 3y
2
 and 2x
2
 - y
2
 + 9 
= (x
2
 - 3y
2
) + (2x
2
 - y
2
 + 9) 
= x
2
 + 2x
2
 - 3y
2
 - y
2
+ 9 
= 3x
2
 - 4y
2
 + 9 
Now, required expression = (x
2
 + 2xy + y
2
) + (3x
2
 - 4y
2
 + 9) 
= x
2
 + 3x
2
 + 2xy + y
2
 - 4y
2
 + 9 
= 4x
2
 + 2xy  - 3y
2
+ 9 
 
9. Add a
3
+ b
3
 - 3 to the sum of 2a
3
 - 3b
3 
- 3ab + 7 and -a
3
 + b
3
 + 3ab - 9. 
 
Solution: 
Given a
3
+ b
3
 – 3, 2a
3
 - 3b
3 
- 3ab + 7 and -a
3
 + b
3
 + 3ab - 9. 
First, we need to find the sum of 2a
3
 - 3b
3
- 3ab + 7 and - a
3
 + b
3
 + 3ab - 9. 
= (2a
3
 - 3b
3
- 3ab + 7) + (- a
3
 + b
3
 + 3ab - 9) 
Collecting positive and negative like terms together, we get 
= 2a
3
 - a
3
- 3b
3
+ b
3
 - 3ab + 3ab + 7 - 9 
= a
3
 - 2b
3
 - 2 
Now, the required expression = (a
3
 + b
3
 - 3) + (a
3
 - 2b
3
 - 2). 
= a
3
+ a
3
+ b
3
- 2b
3
 - 3 - 2 
= 2a
3
 - b
3
 - 5 
 
10. Subtract: 
(i) 7a
2
b from 3a
2
b 
(ii) 4xy from -3xy 
 
Solution: 
(i) Given 7a
2
b from 3a
2
b 
 
 
 
 
 
 
 
= 3a
2
b -7a
2
b 
= (3 -7) a
2
b 
= - 4a
2
b 
 
(ii) Given 4xy from -3xy 
= –3xy – 4xy 
= –7xy 
 
11. Subtract: 
(i) - 4x from 3y 
(ii) - 2x from – 5y 
 
Solution: 
(i) Given - 4x from 3y 
= (3y) – (–4x) 
= 3y + 4x 
 
(ii) Given - 2x from – 5y 
= (-5y) – (–2x) 
= –5y + 2x 
 
12. Subtract: 
(i) 6x
3 
-7x
2 
+ 5x - 3 from 4 - 5x + 6x
2
 - 8x
3
 
(ii) - x
2 
-3z from 5x
2 
– y + z + 7 
(iii) x
3
 + 2x
2
y + 6xy
2
 - y
3
 from y
3
-3xy
2
-4x
2
y 
 
Solution: 
(i) Given 6x
3 
-7x
2 
+ 5x - 3 and 4 - 5x + 6x
2
 - 8x
3
 
= (4 - 5x + 6x
2
 - 8x
3
) - (6x
3
 - 7x
2
 + 5x - 3) 
= 4 - 5x + 6x
2
 - 8x
3
 - 6x
3
 + 7x
2
 - 5x + 3 
= - 8x
3
- 6x
3
 + 7x
2
 + 6x
2
- 5x - 5x + 3 + 4 
= - 14x
3
 + 13x
2
 - 10x +7 
 
(ii) Given - x
2 
-3z and 5x
2 
– y + z + 7 
= (5x
2
 - y + z + 7) - (- x
2
 - 3z)  
= 5x
2
 - y + z + 7 + x
2
 + 3z 
= 5x
2
+ x
2
 - y + z + 3z + 7
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FAQs on Algebraic Expressions (Exercise 7.2) RD Sharma Solutions - Mathematics (Maths) Class 7

1. What are algebraic expressions?
Ans. Algebraic expressions are mathematical expressions that contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. They represent relationships between quantities and can be used to solve various mathematical problems.
2. How do you simplify algebraic expressions?
Ans. To simplify an algebraic expression, you need to combine like terms and perform the indicated operations. This involves adding or subtracting terms with the same variable and exponent, and multiplying or dividing terms with the same variable. By simplifying the expression, you can make it easier to work with and solve equations or problems.
3. What is the difference between an equation and an algebraic expression?
Ans. An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations, but it does not have an equal sign. On the other hand, an equation is a statement that shows the equality of two expressions. Equations are solved to find the value of the variable that makes the equation true, while expressions are simplified or evaluated.
4. How can algebraic expressions be used in real-life situations?
Ans. Algebraic expressions can be used to represent and solve various real-life situations. For example, they can be used to calculate the cost of items with discounts, determine the area or volume of objects, solve problems related to time and distance, or analyze patterns and relationships in data. By using algebraic expressions, we can express and solve problems mathematically.
5. What are some common mistakes to avoid when simplifying algebraic expressions?
Ans. When simplifying algebraic expressions, it is important to avoid common mistakes such as: - Forgetting to apply the distributive property correctly. - Combining terms with different variables or exponents. - Making errors in performing the operations of addition, subtraction, multiplication, or division. - Forgetting to simplify terms with coefficients or constants. - Not following the correct order of operations (PEMDAS/BODMAS) while simplifying the expression.
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Document Description: RD Sharma Solutions: Algebraic Expressions (Exercise 7.2) for Class 7 2024 is part of Mathematics (Maths) Class 7 preparation. The notes and questions for RD Sharma Solutions: Algebraic Expressions (Exercise 7.2) have been prepared according to the Class 7 exam syllabus. Information about RD Sharma Solutions: Algebraic Expressions (Exercise 7.2) covers topics like and RD Sharma Solutions: Algebraic Expressions (Exercise 7.2) Example, for Class 7 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for RD Sharma Solutions: Algebraic Expressions (Exercise 7.2).
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