Algebraic Expressions (Exercise 7.3) RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download

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Exercise 7.3         Page No: 7.16 
 
1. Place the last two terms of the following expressions in parentheses preceded by a 
minus sign: 
(i) x + y – 3z + y     
(ii) 3x – 2y – 5z – 4 
(iii) 3a – 2b + 4c – 5 
(iv) 7a + 3b + 2c + 4 
(v) 2a
2 
- b
2
 - 3ab + 6 
(vi) a
2
 + b
2
 - c
2
 + ab - 3ac 
 
Solution: 
(i) Given x + y – 3z + y      
x + y – 3z + y = x + y – (3z – y) 
 
(ii) Given 3x – 2y – 5z – 4 
3x – 2y – 5z – 4 = 3x – 2y – (5z + 4) 
 
(iii) Given 3a – 2b + 4c – 5 
3a – 2b + 4c – 5 = 3a – 2b – (–4c + 5) 
 
(iv) Given 7a + 3b + 2c + 4 
7a + 3b + 2c + 4 = 7a + 3b – (–2c – 4) 
 
(v) Given 2a
2 
- b
2
 - 3ab + 6 
2a
2 
- b
2
 - 3ab + 6 = 2a
2
 - b
2
 - (3ab - 6) 
 
(vi) Given a
2
 + b
2
 - c
2
 + ab - 3ac  
a
2
 + b
2
 - c
2 
+ ab - 3ac = a
2
 + b
2
 - c
2
 - (- ab + 3ac) 
 
2. Write each of the following statements by using appropriate grouping symbols: 
(i) The sum of a – b and 3a – 2b + 5 is subtracted from 4a + 2b – 7. 
(ii) Three times the sum of 2x + y – [5 – (x – 3y)] and 7x – 4y + 3 is subtracted from 3x – 
4y + 7 
(iii) The subtraction of x
2 
- y
2
 + 4xy from 2x
2
 + y
2
 - 3xy is added to 9x
2
 - 3y
2
- xy. 
 
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Exercise 7.3         Page No: 7.16 
 
1. Place the last two terms of the following expressions in parentheses preceded by a 
minus sign: 
(i) x + y – 3z + y     
(ii) 3x – 2y – 5z – 4 
(iii) 3a – 2b + 4c – 5 
(iv) 7a + 3b + 2c + 4 
(v) 2a
2 
- b
2
 - 3ab + 6 
(vi) a
2
 + b
2
 - c
2
 + ab - 3ac 
 
Solution: 
(i) Given x + y – 3z + y      
x + y – 3z + y = x + y – (3z – y) 
 
(ii) Given 3x – 2y – 5z – 4 
3x – 2y – 5z – 4 = 3x – 2y – (5z + 4) 
 
(iii) Given 3a – 2b + 4c – 5 
3a – 2b + 4c – 5 = 3a – 2b – (–4c + 5) 
 
(iv) Given 7a + 3b + 2c + 4 
7a + 3b + 2c + 4 = 7a + 3b – (–2c – 4) 
 
(v) Given 2a
2 
- b
2
 - 3ab + 6 
2a
2 
- b
2
 - 3ab + 6 = 2a
2
 - b
2
 - (3ab - 6) 
 
(vi) Given a
2
 + b
2
 - c
2
 + ab - 3ac  
a
2
 + b
2
 - c
2 
+ ab - 3ac = a
2
 + b
2
 - c
2
 - (- ab + 3ac) 
 
2. Write each of the following statements by using appropriate grouping symbols: 
(i) The sum of a – b and 3a – 2b + 5 is subtracted from 4a + 2b – 7. 
(ii) Three times the sum of 2x + y – [5 – (x – 3y)] and 7x – 4y + 3 is subtracted from 3x – 
4y + 7 
(iii) The subtraction of x
2 
- y
2
 + 4xy from 2x
2
 + y
2
 - 3xy is added to 9x
2
 - 3y
2
- xy. 
 
 
 
 
 
 
 
 
Solution: 
(i) Given the sum of a – b and 3a – 2b + 5 = [(a – b) + (3a – 2b + 5)]. 
This is subtracted from 4a + 2b – 7. 
Thus, the required expression is (4a + 2b – 7) – [(a – b) + (3a – 2b + 5)] 
 
(ii) Given three times the sum of 2x + y – {5 – (x – 3y)} and 7x – 4y + 3 = 3[(2x + y – {5 – (x 
– 3y)}) + (7x – 4y + 3)] 
This is subtracted from 3x – 4y + 7. 
Thus, the required expression is (3x – 4y + 7) – 3[(2x + y – {5 – (x – 3y)}) + (7x – 4y + 3)] 
 
(iii) Given the product of subtraction of x
2
- y
2
 + 4xy from 2x
2
 + y
2
 - 3xy is given by {(2x
2
 + 
y
2
 - 3xy) – (x
2
-y
2
 + 4xy)} 
When the above equation is added to 9x
2
 - 3y
2 
- xy, we get 
{(2x
2
 + y
2
 - 3xy) – (x
2 
- y
2 
+ 4xy)} + (9x
2 
- 3y
2
- xy)) 
This is the required expression.