RS Aggarwal Solutions for Class 8 Maths Chapter 6 Exercise 6.2 Operations on Algebraic Expressions

The PDF link for RS Aggarwal Solutions for Class 8 Maths Chapter 6 Exercise 6.2 is available below. By referring to this PDF students can gain a clearer understanding of how to simplify and expand algebraic expressions, reinforcing their skills in this area. This will help improve their problem-solving abilities and overall performance in mathematics.

RS Aggarwal Solutions for Class 8 Maths Chapter 6 Exercise 6.2 PDF

RS Aggarwal Solutions for Class 8 Maths Chapter 6 Exercise 6.1 (Exercise 6B)

RS Aggarwal Solutions for Class 8 Maths Chapter 6 Exercise 6.2 are available below. This resource provides detailed solutions and explanations for problems related to operations on algebraic expressions.

Find each the following products:

(Question 1) (5x + 7) × (3x + 4)

Solution:

= (5x × 3x) + (7 × 3x) + (5x × 4) + (7 × 4) = 15x ² + 21x + 20x + 28 = 15x ² + 41x + 28

(Question 2) (4x + 9) × (x – 6)

Solution:

= (4x × x) + (9 × x) – (4x × 6) – (9 × 6) = 4x ² + 9x – 24x – 54 = 4x ² – 15x – 54

(Question 3) (2x + 5) × (4x – 3)

Solution:

= (2x × 4x) + (5 × 4x) – (2x × 3) – (5 × 3) = 8x ² + 20x – 6x – 15 = 8x ² + 14x – 15

(Question 4) (3y – 8) × (2m – 3n)

Solution:

= (3y × 2m) – (8 × 2m) – (3y × 3n) + (8 × 3n) = 6ym – 16m – 9yn + 24n

(Question 5) (7x + 2y) × (x + 4y)

Solution:

= (7x × x) + (2y × x) + (7x × 4y) + (2y × 4y) = 7x ² + 2xy + 28xy + 8y ² = 7x ² + 30xy + 8y ²

(Question 6) (9x + 5y) × (4x × 3y)

Solution:

= (9x × 4x) + (5y × 4x) + (9x × 3y) + (5y × 3y) = 36x ² + 20xy + 27xy + 15y ²

(Question 7) (3m – 4n) × (2m – 3n)

Solution:

= (3m × 2m) – (4n × 2m) – (3m × 3n) + (4n × 3n) = 6m ² – 8mn – 9mn + 12n ² = 6m ² – 17mn + 12n ²

(Question 8) (x ² – a ² ) × (x – a)

Solution:

= (x ² × x) – (a ² × x) – (x ² × a) + (a ² × a) = x ³ + a ² x – ax ² + a ³

(Question 9) (x ² – y ² ) × (x + 2y)

Solution:

= (x ² × x) – (y ² × x) + (x ² × 2y) – (y ² × y) = x ³ – xy ² + 2x ² y – y ³

(Question 10) (3p ² + q ² ) × (2p ² – 3q ² )

Solution:

= (3p ² × 2p ² ) + (q ² × 2p ² ) – (3p ² × 3q ² ) – (q ² × 3q ² ) = 6p ⁴ + 2p ² q ² – 9p ² q ² – 3q ⁴ = 6p ⁴ – 7p ² q ² – 3q ⁴

(Question 11) (2x ² – 5y ² ) × (x ² + 3y ² )

Solution:

= (2x ² × x ² ) – (5y ² × x ² ) + (2x ² × 3y ² ) – (5y ² × 3y ² ) = 2x ⁴ – 5x ² y ² + 6x ² y ² – 15y ⁴ = 2x ⁴ + x ² y ² – 15y ⁴

(Question 12) (x ³ – y ³ ) × (x ² + y ² )

Solution:

= (x ³ × x ² ) – (y ³ × x ² ) + (x ³ × y ² ) – (y ³ × y ² ) = x ⁵ – x ² y ³ + x ³ y ² – y ⁵

(Question 13) (x ⁴ + y ⁴ ) × (x ² – y ² )

Solution:

= (x ⁴ × x ² ) + (y ⁴ × x ² ) – (x ⁴ × y ² ) – (y ⁴ × y ² ) = x ⁶ + x ² y ⁴ – x ⁴ y ² – y ⁶

Find each of the following products:

(Question 15) (x ² – 3x + 7) × (2x + 3)

Solution:

= (x ² × 2x) – (3x × 2x) + (7 × 2x) + (x ² × 3) – (3x × 3) + (7 × 3) = 2x ³ – 6x ² + 14x + 3x ² – 9x + 21 = 2x ³ – 3x ² + 5x + 21

(Question 16) (3x ² + 5x – 9) × (3x – 5)

Solution:

= (3x ² × 3x) + (5x × 3x) – (9 × 3x) – (3x ² × 5) – (5x × 5) + (9 × 5) = 9x ³ + 15x ² – 27x – 15x ² – 25x + 45 = 9x ³ – 52x + 45

(Question 17) (x ² – xy + y ² ) × (x + y)

Solution:

= (x ² × x) – (xy × x) + (y ² × x) + (x ² × y) – (xy × y) + (y ² × y) = x ³ – x ² y + y ² x + x ² y – xy ² + y ³ = (x ³ + y ³ )

(Question 18) (x ² + xy + y ² ) × (x – y)

Solution:

= (x ² × x) + (xy × x) + (y ² × x) – (x ² × y) – (xy × y) – (y ² × y) = x ³ + x ² y + xy ² – x ² y – xy ² – y ³ = (x ³ – y ³ )

(Question 19) (x ³ – 2x ² + 5) × (4x – 1)

Solution:

= (x ³ × 4x) – (2x ² × 4x) + (5 × 4x) – x ³ + 2x ² – 5 = 4x ⁴ – 8x ³ + 20x – x ³ + 2x ² – 5 = 4x ⁴ – 9x ³ + 2x ² + 20x – 5

(Question 20) (9x ² – x + 15) × (x ² – 3)

Solution:

= (9x ² × x ² ) – (x × x ² ) + (15 × x ² ) – (9x ² × 3) + 3x – 45 = 9x ⁴ – x ³ + 15x ² – 27x ² + 3x – 45 = 9x ⁴ – x ³ – 12x ² + 3x – 45

(Question 21) (x ² – 5x + 8) × (x ² + 2)

Solution:

= (x ² × x ² ) – (5x × x ² ) + 8x ² + 2x ² – 10x + 16 = x ⁴ – 5x ³ + 10x ² – 10x + 16

(Question 22) (x ³ – 5x ² + 3x + 1) × (x ² – 3)

Solution:

= (x ³ × x ² ) – (5x ² × x ² ) + (3x × x ² ) + x ² – 3x ³ + 15x ² – 9x – 3 = x ⁵ – 5x ⁴ + 3x ³ + x ² – 3x ³ + 15x ² – 9x – 3 = x ⁵ – 5x ⁴ + 16x ² – 9x – 3

(Question 23) (3x + 2y – 4) × (x – y + 2)

Solution:

= 3x ² + 2xy – 4x – 3xy – 2y ² + 4y + 6x + 4y – 8 = 3x ² – xy + 2x – 2y ² + 8y – 8

(Question 24) (x ² – 5x + 8) × (x ² + 2x – 3)

Solution:

= x ⁴ – 5x ³ + 8x ² + 2x ³ – 10x ² + 16x – 3x ² + 15x – 24 = x ⁴ – 3x ³ – 5x ² + 31x – 24

(Question 25) (2x ² + 3x – 7) × (3x ² – 5x + 4)

Solution:

= 6x ⁴ + 9x ³ – 21x ² – 10x ³ – 15x ² + 35x + 8x ² + 12x – 28 = 6x ⁴ – x ³ – 28x ² + 47x – 28

(Question 26) (9x ² – x + 15) × (x ² – x – 1)

Solution:

= 9x ⁴ – x ³ + 15x ² – 9x ³ + x ² – 15x – 9x ² + x – 15 = 9x ⁴ – 10x ³ + 7x ² – 14x – 15