DAV Class 6 Maths Chapter 6 Worksheet 5 Solutions

The DAV Class 6 Maths Solutions and DAV Class 6 Maths Chapter 6 Worksheet 5 Solutions of Introduction to Algebra offer comprehensive answers to textbook questions.

DAV Class 6 Maths Ch 6 WS 5 Solutions

Question 1.
Add the following monomials:

(а) 3x, 5x, 2x
Solution:
3x + 5x + 2x = 10x

(b) 5a, a, – 7a
Solution:
5a + a + (- 7a) = 5a + a – 7a
= 6a – 7a
= – a

(c) 2abc, – abc, 5abc
Solution:
2abc + (- abc) + 5abc
= 2abc – abc + 5abc
= 6abc

(d) – 2xy, 7xy, 15xy, – 10xy, xy, – xy
Solution:
– 2xy + 7xy + 15xy – 10xy + xy – xy = 10 xy

(e) 3a, 4b, – 6a, – 2b, – 5a, 10b
Solution:
3a + 4b + (- 6a) + (- 2b) + (- 5a) + 10b
= (3a – 6a – 5b) + (4b – 2b + 10b)
= – 8a + 12b

(f) a, 6a, – 2b, 5c, – 2c
Solution:
a + 6a + (- 2b) + 5c + (-2c)
= (a + 6a) + (- 2b) + (5c – 2c)
= 7a – 2b + 3c

Question 2.
Find the sum using column method.

(а) 7a + 2b and 3a + 4b
Solution:

(b) 2x² – y² and 3x² + 5y²
Solution:

(c) – 4x – 5y and 3x – 8y
Solution:

(d) 4x + 3y + 5xy, 2x + 10y – 2xy and – 3x – 3y
Solution:

(e) -2a + 3b, 5a + 2b – c and – a – b – c
Solution:

(f) 3x² + 4y², 2y² + 2xy – x², x² + 2y²
Solution:

Question 3.
Add using horizontal method:

(а) 7x + 3y and – 4x – 2y
Solution:
7x + 3y and (- 4x – 2y)
= (7x – 4x) + (3y – 2y)
= 3x + y

(b) 3a – 2b + c + 3 and a + 3b – 2c – 4
Solution:
3a – 2b + c + 3 and a + 3b – 2c – 4
= (3a – 2b + c + 3) + (a + 3b – 2c – 4)
= 3a – 2b + c + 3 + a + 3b – 2c – 4
= (3a + a) + (- 2b + 3b) + (c – 2c) + (3 – 4)
= 2a + b – c – 1

(c) a² + 2ab + b² and a² – 2ab + b²
Solution:
a² + 2ab + b² and a² – 2ab + b²
= (a² + 2ab + b²) + (a² – 2ab + b²)
= a² + 2ab + b² + a² – 2ab + b²
= (a² + a²) + (2ab – 2ab) + (b² + b²)
= 2a² + 0 + 2b²
= 2a² + 2b²

(d) xy – yz + 2, 2yz + xy – 7 and 3xy + 3yz + 3
Solution:
xy – yz + 2, 2yz + xy – 7 and 3xy + 3yz + 3
= (xy – yz + 2) + (2yz + xy – 7) + (3xy + 3yz + 3)
= xy – yz + 2 + 2yz + xy – 7 + 3xy + 3yz + 3
= (xy + xy + 3xy) + {-yz + 2yz + 3yz) + (2 – 7 + 3)
= 5xy + 4yz – 2

(e) – 2x² + 3y², 3y² + 3 – x² and x² + y² + 5 – 3xy
Solution:
– 2x² + 3y², 3y² + 3 – x² and x² + y² + 5 – 3xy
= – 2x² + 3y² + 3y² + 3 – x² + x² + y² + 5 – 3xy
= (- 2x² – x² + x²) + (3y² + 3y² + y²) + (- 3xy) + (3 + 5)
= – 2x² + 7y² – 3xy + 8

(f) 3pq + 2pr – 4qr, – pq + 2qr + pr and 4pq – 3pr + 2qr
Solution:
3pq + 2pr – 4qr, -pq + 2qr + pr and 4pq – 3pr + 2qr
= (3pq + 2pr – 4qr) + (- pq + 2qr + pr) + (4pq – 3pr + 2qr)
= 3pq + 2pr – 4qr – pq + 2qr + pr + 4pq – 3pr + 2qr
= (3pq – pq + 4pq) + (- 4qr + 2qr + 2qr) + (2pr + pr – 3pr)
= 6pq + 0
= 6pq