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
