DAV Class 6 Maths Chapter 6 Worksheet 6 Solutions

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

DAV Class 6 Maths Ch 6 WS 6 Solutions

Question 1.
Subtract:

(a) 3x from 5x
Solution:
3x from 5x = 5x – 3x = 2x

(b) 4a from 3a
Solution:
4a from 3a = 3a – 4a = – a

(c) 13x² from x²
Solution
13x² from x² = x² – 13x²
= – 12x²

(d) – y from 3y
Solution:
– y from 3y = 3y – (- y)
= 3y + y
= 4y

(e) – 7a from – 3a
Solution:
– 7a from – 3a = – 3a (-7a)
= – 3a + 7a
= 4a

(f) 3abc from – 3 abc
Solution:
3abc from – 3abc = (- 3 abc) – (3abc)
= – 6abc

Question 2.
Subtract by column method:

(a) 3x + 3y from 2x + 3y
Solution:

(b) a² + 2b² from 3b² – 4a²
Solution:

(c) 5x²y – 3xy² from – 2x²y + 4y²
Solution:

(d) 2a – 3b + 5 from 5a – b – 2
Solution:

(e) p + q – r from – p – q – r
Solution:

= – 2p – 2q

(f) a³ + b³ – 3abc from – a³ + b³ + 3abc
Solution:

= – 2a³

Question 3.
Subtract by horizontal method:

(a) 2x – 3y + 4z from 4x – 6y – z
Solution:
2x – 3y + 4z from 4x – 6y – z
= (4x – 6y – z) – (2x – 3y + 4z)
= 4x – 6y – z – 2x + 3y – 4z
= 2x – 3y – 5z

(b) 2x – 4y from – 4x + 3y
Solution:
2x – 4y from – 4x + 3y
= (- 4x + 3y) – (2x – 4y)
= – 4x + 3y – 2x + 4y
= – 6x + 7y

(c) 5q² – p² – 7r from 6p² – q² + 2r – 9
Solution:
5q² – p² – 7r from 6p² – q² + 2r – 9
(6p² – q² + 2r – 9) – (5q² – p² – 7r)
= 6p² – q² + 2r – 9 – 5q² + p² + 7r
= (6p² + p²) + (- q² – 5q²) + (2r + 7r) – 9
= 7p² – 6q² + 9r – 9

(d) – x – y from x + y
Solution:
– x – y from x + y
= (x + y) – (-x – y)
= – x + y + x + y
=> (x + x) + (y + y) = 2x + 2y

(e) 7pqr – 8p + 3 from 10 – 4pqr + 3p
Solution:
7pqr – 8p + 3 from 10 – 4pqr + 3p
= (10 – 4pqr + 3p) – (7pqr – 8p + 3)
= 10 – 4pqr + 3p – 7pqr + 8p – 3
= (10 – 3) + (- 4pqr – 7pqr) + (3p + 8p)
= 7 – 11pqr + 11p

(f) 5x³ + 3x² – x – 3 from 5x³ – 3x² + 2x – 3
Solution:
5x³ + 3x² – x – 3 from 5x³ – 3x² + 2x – 3
(5x² – 3x² + 2x – 3) – (5x³ + 3x²2 – x – 3)
= 5x² – 3x² + 2x – 3 – 5x³ – 3x² + x + 3
= – 5x³ + (5x² – 3x² – 3x²) + (2x + x) + (- 3 + 3)
= – 5x³ – x² + 3x + 0
= – 5x³ – x² + 3x

Question 4.
Subtract 3x + 2y – 5xy from 0.
Solution:
0 – (3x + 2y – 5xy)
= 0 – 3x – 2y + 5x.y
= – 3x – 2y + 5 xy

Question 5.
From the sum of x² + x + 1 and x² – x + 1, subtract – x² – x + 1.
Solution:
[(x² + x + 1) + (x² – x + 1)] – (- x² – x + 1)
= (x² + x + 1 + x² – x + 1) – (- x² – x + 1)
= x² + x + 1 + x² – x + 1 + x² + x – 1
= (x² + x² + x²) + (x – x + x) + (1 + 1 – 1)
= 3x² + x + 1

Question 6.
Subtract the sum of 2a + 3b, a – 2b + c, – a + 2c and 4a + 2b – 5 from 6a – 4b + 8.
Solution:
First we find the sum of 2a + 3b, a – 2b + c, – a + 2c and 4a + 2b – 5.
= (2a + 3b) + (a – 2b + c) + (- a + 2c) + (4a + 26-5)
= 2a + 3b + a – 2b + c – a + 2c + 4a + 26-5
= (2a + a – a + 4a) + (3b – 2b + 2b) + (c + 2c) – 5
= 6a + 3b + 3c – 5
Now subtract 6a + 3b + 3c – 5 from 6a – 4b + 8
= 6a – 4b + 8

= – 7b – 3c + 13