# RS Aggarwal Class 7 Solutions Chapter 6 Algebraic Expressions Ex 6D

Here you can get solutions of RS Aggarwal Solutions For Class 7 Solutions Chapter 6 Algebraic Expressions Ex 6D. These Solutions are part of RS Aggarwal Solutions For Class 7 Solutions Chapter 6 Algebraic Expressions Ex 6D. we have given RS Aggarwal Solutions For Class 7 Solutions Chapter 6 Algebraic Expressions Ex 6D download pdf.

## RS Aggarwal Class 7 Solutions Chapter 6 Algebraic Expressions Ex 6D

Other Exercises

Find each of the following products.
Question 1.
Solution:
(5x + 7) (3x + 4)
= 5x (3x + 4) + 7 (3x + 4)
= 5x x 3x + 5x x 4 + 7 x 3x + 7 x 4
= 15x2 + 20x + 21x + 28
= 15x2 + 41x + 28

Question 2.
Solution:
(4x – 3) (2x + 5)
= 4x (2x + 5) – 3 (2x + 5)
= 4x x 2x + 4x x 5 – 3 x 2x -3 x 5
= 8x2 + 20x – 6x – 15
= 8x2 + 14x – 15

Question 3.
Solution:
(x – 6) (4x + 9)
= x (4x + 9) – 6 (4x + 9)
= x x 4x + x x 9 – 6 x 4x – 6 x 9
= 4x2 + 9x – 24x – 54
= 4x2 – 15x – 54

Question 4.
Solution:
(5y – 1) (3y – 8)
= 5y x 3y – 5y x 8 – 1 x 3y – 8 x (-1)
= 15y2 – 40y – 3y + 8
= 15y2 – 43y + 8

Question 5.
Solution:
(7x + 2y) (x + 4y)
= 7x (x + 4y) + 2y (x + 4y)
= 7x x x + 7x x 4y + 2y x x + 2y x 4y
= 7x2 + 28xy + 2xy + 8y2
= 7x2 + 30xy + 8y2

Question 6.
Solution:
(9x + 5y) (4x + 3y)
= 9x (4x + 3y) + 5y (4x + 3y)
= 9x x 4x + 9x x 3y + 5y x 4x + 5y x 3y
= 36x2 + 27xy + 20xy + 15y2
= 36x2 + 47xy +15y2

Question 7.
Solution:
(3m – 4n) (2m – 3n)
= 3m (2m – 3n) – 4n (2m – 3n)
= 3m x 2m – 3m x 3n – 4n x 2m – 4n x (-3n)
= 6m2 – 9mn – 8mn + 12n2
= 6m2 – 17mn + 12n2

Question 8.
Solution:
(0.8x – 0.5y) (1.5x – 3y)
= 0.8x (1.5x – 3y) – 0.5y (1.5x – 3y)
= 0.8x x 1.5x – 0.8x x 3y – 0.5y x 1.5x – 0.5y x (-3y)
= 1.20x2 – 2.4xy – 0.75xy + 1.5y2
= 1.2x2 – 3.15xy + 1.5y2

Question 9.
Solution:

Question 10.
Solution:

Question 11.
Solution:

Question 12.
Solution:
(x2 – a2) (x – a)
= x2 (x – a) – a2 (x – a)
= x2 x x – x2 x a – a2 x x – a2 (-a)
= x3 – xa – xa2 + a3

Question 13.
Solution:
(3p2 + q2) (2p2 – 3q2)
= 3p2 (2p2 – 3q2) + q2 (2p2 – 3q2)
= 3p2 x 2p2 – 3p2 x 3q2 + q2 x 2p2 – q2 x 3q2
= 6q4 – 9p2q2 + 2p2q2 – 3q4
= 6p4 – 7p2q2 – 3q4

Question 14.
Solution:
(2x2 – 5y2) (x2 + 3y2)
= 2x2 (x2 + 3y2) – 5y2 (x2 + 3y2)
= 2x2 x x2 + 2x2 x 3y2 – 5y2 x x2 – 5y2 x 3y2
= 2x4 + 6xy2 – 5xy2 – 15y4
= 2y4 + xy2 – 15y4

Question 15.
Solution:
(x3 – y3) (x2 + y2)
= x3 (x2 + y2) – y3 (x2 + y2)
= x3 x x2 + x3 x y2 – y3 x x2 – y3 x y2
= x5 + xy2 – xy3 – y5

Question 16.
Solution:
(x4 + y4) (x2 – y2)
= x4 (x2 – y2) + y4 (x2 – y2)
= x4 x x2 – x4 x y2 + y4 x x2 – y4 x y2
= x6 – xy2 + xy4 – y6

Question 17.
Solution:

Question 18.
Solution:
(x2 – y2) (x + 2y)
= x2 (x + 2y) – y2 (x + 2y)
= x2 x x + x2 x 2y – y2 x x – y2 x 2y
= x3 + 2xy – xy2 – 2y3

Question 19.
Solution:
(2x + 3y – 5) (x + y)
= 2x (x + y) + 3y (x + y) – 5 (x + y)
= 2x x x + 2x x y + 3y x x + 3y x y – 5 x x – 5 x y
= 2x2 + 2xy + 3xy + 3y2 – 5x – 5y
= 2x2 + 5xy + 3y2 – 5x – 5y

Question 20.
Solution:
(3x + 2y – 4) (x – y)
= 3x (x – y) + 2y (x – y) – 4 (x – y)
= 3x x x – 3x x y + 2y x x – 2y x y – 4 x x – 4 x (-y)
= 3x2 – 3xy + 2xy – 2y2 – 4x + 4y
= 3x2 – xy – 2y2 – 4x + 4y

Question 21.
Solution:
(x2 – 3x + 7) (2x + 3)
= x2 (2x + 3) – 3x (2x + 3) + 7 (2x + 3)
= x2 x 2x + x2 x 3 – 3x x 2x – 3x x 3 + 7 x 2x + 7 x 3
= 2x3 + 3x2 – 6x2 – 9x + 14x + 21
= 2x3 – 3x2 + 5x + 21

Question 22.
Solution:
(3x2 + 5x – 9) (3x – 9)
= 3x2 (3x – 9) + 5x (3x – 9) – 9 (3x – 9)
= 3x2 x 3x – 3×2 x 9 + 5x x 3x + 5x x (-9) – 9 x 3x – 9 x (-9)
= 9x3 – 27x2 + 15x2 – 45x – 27x + 81
= 9x3 – 12x2 – 72x + 81

Question 23.
Solution:
(9x2 – x + 15) (x2 – 3)
= 9x2 (x2 – 3) – x (x2 – 3) + 15 (x2 – 3)
= 9x2 x x2 – 9x2 x 3 – x x x2 + x x 3 + 15 x x2 – 15 x 3
= 9x4 – 27x2 – x3 + 3x + 15x2 – 45
= 9x4 – x3 – 12x2 + 3x – 45

Question 24.
Solution:
(x2 + xy + y2) (x – y)
= x2 (x – y) + xy (x – y) + y2 (x – y)
= x2 x x – x2 x y + xy x x – xy x y + y2 x x – y2 x y
= x3 – x2y + x2y – xy2 + xy2 – y2
= x3 – y3

Question 25.
Solution:
(x2 – xy + y2) (x + y)
= x2 (x + y) – xy (x + y) + y2 (x + y)
= x3 + xy – xy – xy2 + xy2 + y3
= x3 + y3

Question 26.
Solution:
(x2 – 5x + 8) (x2 + 2)
= x2 (x2 + 2) – 5x (x2 + 2) + 8 (x2 + 2)
= x2 x x2 + x2 x 2 – 5x x x2 – 5x x 2 + 8 x x2 + 8 x 2
= x4 + 2x2 – 5x3 – 10x + 8x2 + 16
= x4 – 5x3 + 2x2 + 8x2 – 10x + 16
= x4 – 5x3 + 10x2 – 10x + 16

Simplify:
Question 27.
Solution:
(3x + 4) (2x – 3) + (5x – 4) (x + 2)
= [3x (2x – 3) + 4 (2x – 3)] + [5x (x + 2) – 4 (x + 2)]
= [3x x 2x – 3x x 3 + 4 x 2x – 4 x 3] + [5x x x + 5x x 2 – 4 x x – 4 x 2]
= [6x2 – 9x + 8x – 12] + [5x2 + 10x – 4x – 8]
= (6x2 – x – 12) + (5x2 + 6x – 8)
= 6x2 – x – 12 + 5x2 + 6x – 8
= 6x2 + 5x2 – x + 6x – 12 – 8
= 11x2 + 5x – 20

Question 28.
Solution:
(5x – 3) (x + 4) – (2x + 5) (3x – 4)
= [5x x x + 5x x 4 – 3 x x – 3 x 4] – [2x x 3x + 2x x (-4) + 5 x 3x + 5x (-4)]
= [5x2 + 20x – 3x – 12] – [6x2 – 8x + 15x – 20]
= (5x2 + 17x – 12) – (6x2 + 7x – 20)
= 5x2 + 17x – 12 – 6x2 – 7x + 20
= 5x2 – 6x2 + 17x – 7x – 12 + 20
= -x2 + 10x + 8

Question 29.
Solution:
(9x – 7) (2x – 5) – (3x – 8) (5x – 3)
= [9x (2x – 5) -7 (2x – 5)] – [3x (5x – 3) -8 (5x – 3)]
= [9x x 2x – 9x x 5 – 7 x 2x – 7 x (-5)] – [3x x 5x – 3x x 3 – 8 x 5x – 8 x (-3)]
= [18x2 – 45x – 14x + 35] – [15x2 – 9x – 40x + 24]
= 18x2 – 45x – 14x + 35 – 15x2 + 9x + 40x – 24
= 18x2 – 15x2 – 45x – 14x + 9x + 40x + 35 – 24
= 3x2 – 59x + 49x + 11
= 3x2 – 10x + 11

Question 30.
Solution:
(2x + 5y) (3x + 4y) – (7x + 3y) (2x + y)
= [2x (3x + 4y) + 5y (3x + 4y)] – [7x (2x + y) + 3y (2x + y)]
= [2x x 3x + 2x x 4y + 5y x 3x + 5y x 4y] – [7x x 2x + 7x x y + 3y x 2x + 3y x y]
= [6x2 + 8xy + 15xy + 20y2] – [14x2 + 7xy + 6xy + 3y2]
= [6x2 + 23xy + 20y2] – [14x2 + 13xy + 3y2]
= 6x2 + 23xy + 20y2 – 14x2 – 13xy – 3y2
= 6x2 – 14x2 + 23xy – 13xy + 20y2 – 3y2
= -8x2 + 10xy + 11y2

Question 31.
Solution:
(3x2 + 5x – 7) (x – 1) – (x2 – 2x + 3) (x + 4)
= [3x2 (x – 1) + 5x (x – 1) – 7 (x – 1)] – [x2 (x + 4) – 2x (x + 4) + 3 (x + 4)]
= [3x2 x x – 3x2 x 1 + 5x x x – 5x x (-1) – 7 x x -7 x (-1)] -[x2 x x + x2 x 4 – 2x x x – 2x x 4 + 3 x x + 3 x 4]
= [3x3 – 3x2 + 5x2 – 5x – 7x + 7] – [x3 + 4x2 – 2x2 – 8x + 3x + 12]
= [3x3 + 2x2 – 12x + 7] – [x3 + 2x2 – 5x + 12]
= 3x3 + 2x2 – 12x + 7 – x3 – 2x2 + 5x – 12
= 3x3 – x3 + 2x2 – 2x2 – 12x + 5x – 12 + 7
= 2x3 – 7x – 5

Complete RS Aggarwal Solutions Class 7

If You have any queries regarding this chapter, please comment on the below section our team will answer you. We tried our best to give complete solutions so you got good marks in your exam.

If these solutions have helped you, you can also share ncertsolutionsfor.com to your friends.

Best of Luck For Your Future!!