The DAV Class 7 Maths Solutions and **DAV Class 7 Maths Chapter 6 Worksheet 6** Solutions of Algebraic Expressions offer comprehensive answers to textbook questions.

## DAV Class 7 Maths Ch 6 WS 6 Solutions

(i) (x + y) (2x + 3y) – (x + y) (x + 1)

Answer:

(x + y)(2x + 3y) – (x + y)(x + 1)

= (x + y) [(2x + 3y) – (x + 1)]

= (x + y)(2x + 3y – x – 1)

= (x + y)(x + 3y- 1)

(ii) 9x(6x – 5y) – 12x^{2}(6x – 5y)

Answer:

9x(6x – 5y) – 12x^{2}(6x – 5y)

= 3x(6x – 5y) (3 – 4x)

(iii) x^{3} (a – 2b) + x^{2} (a – 2b)

Answer:

x^{3}(a – 2b) + x^{2}(a – 2b)

= x^{2}(a – 2b) (x + 1)

(iv) (a – b)^{2} + (a – b)

Answer:

(a – b)^{2} + (a – b)

= (a – b) (a – b + 1)

(v) 3a(p – 2q) – b (p – 2q)

Answer:

3a(p – 2q) – b(p – 2q)

= (p – 2q)(3a – b)

(vi) 8(5x + 9y) + 12(5x + 9y)

Answer:

8(5x + 9y) + 12(5x + 9y)

= 4(5x + 9y) (2 + 3)

= 4(5x + 9y) (5)

= 20(5x + 9 y)

(vii) 1 + x + xy + x^{2}y

Answer:

1 + x + xy + x2y

= (1 + x) + (xy + x2y)

= (1 + x) + xy (1+ x)

= (1 + x) (1 + xy)

(viii) x^{2} +xy + xz + yz

Answer:

x^{2} + xy + xz + yz

= (x^{2} + xy) + (xz + yz)

= x(x + y) + z(x + y)

= (x + y)(x + z)

(ix) a(a + b) + 8a + 8b

Answer:

a(a + b) + 8a + 8b

= a(a + b) + 8 (a + b)

= (a + b) (a + 8)

(x) a^{2} + bc + ac + ab

Answer:

a^{2} + bc + ac + ab

= (a^{2} + ac) + (ab + bc)

= a(a + c) + b(a + c)

= (a + c) (a + b)

(xi) a^{2} + 2a + ab + 2b

Answer:

a^{2} + 2a + ab + 2b

= (a^{2} + 2a) + (ab + 2b)

= a(a + 2) + b(a + 2)

= (a + 2) (a + b)

(xii) ax + ay – bx – by

Answer:

ax+ ay -bx – by

= (ax + ay) – (bx + by)

= a(x + y) – b(x + y)

= (x + y) (a – b)

### DAV Class 7 Maths Chapter 6 Value Based Questions

Question 1.

On the occasion of Van Mahotsav it was decided by the Secretary of Residents Welfare Association to plant saplings of Ashoka trees and Mango trees in the locality. Accordingly Ashoka trees were planted in (3x + 1) rows having (x^{3} + x^{2} – 1) trees in each row and Mango trees were planted in (x – 3) rows having (2x^{2} + 1) trees in each row.

(i) Find the total number of trees planted.

Answer:

Total number of Ashoka trees

= x(2x^{2} + 1) – 3(2x^{2} + 1)

= 2x^{3} + x – 6x^{2} – 3

= 2x^{3} – 6x^{2} + x – 3

Total number of trees planted = Total number of Ashoka trees + Total number of Mango trees

= (3x^{4} + 4x^{3} + x^{2} – 3x – 1) + (2x^{3} – 6x^{2} + x – 3)

= 3x^{4} + 4x^{3} + x^{2} – 3x – 1 + 2x^{3} – 6x^{2} + x – 3

= 3x^{4} + 6x^{3} – 5x^{2} – 2x – 4

(ii) Discuss the importance of trees in our life.

Answer:

Importance of Trees:

Trees make the environment green, fresh and beautiful.

Question 2.

According to a data (p^{2} – 4p + 3) road accidents occurred in City A, (6p – 7 + 2p^{2}) road accidents occurred in City B and (p + 10 + 2p^{2}) road accidents occurred in City C,

(i) Find the total number of road accidents occurred.

Answer:

Total number of road accidents occurred = Road accidents occurred in city A + Road accidents occurred in city B + Road accidents occurred in city C

= (p^{2} – 4p + 3) + (6p – 7 + 2p^{2}) + (p + 10 + 2p^{2})

= 5 p^{2} + 3p + 6

(ii) What should be done to minimise accidents on roads?

Answer:

Traffic rules should be implemented and followed sincerely and defaulters should be penalised.