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

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

These Solutions are part of RS Aggarwal Solutions Class 7. Here we have given RS Aggarwal Solutions Class 7 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

Hope given RS Aggarwal Solutions Class 7 Chapter 6 Algebraic Expressions Ex 6D are helpful to complete your math homework.

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