Gujarat BoardĀ GSEB Textbook Solutions Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.2 Textbook Questions and Answers.
Gujarat Board Textbook Solutions Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.2
Question 1.
Find the product of the following pairs of monomials?
- 4, 7p
- -4p, 7p
- -4p, 7pq
- 4p3, -3p
- 4p, 0
Solution:
1. 4 and 7p
4 Ć 7p = (4 Ć 7) Ć p = 28p
2. -4p and 7p
-4p and 7p = {(-4 Ć 7) Ć p Ć p = -28p2
3. -4p and 7pq
-4p Ć 7pq = (-4 Ć 7) Ć p Ć pq = -28 Ć p2q = -28p2q
4. 4p3 and -3p
4p3 Ć (-3p) = (4 Ć (-3)}p3 Ć p = -12 Ć p4
= -12p4
5. 4p and 0 ā 4p Ć 0 = 0
Question 2.
Find the areas of rectangles with the following pairs of monomlaLc as their lengths and breadths respectively?
(p, q): (10m, 5n); (20x2, 5y2); (4x, 3x2); (3mn, 4np)
Solution:
(i) Length = p
Breadth = q
ā“ Area of the rectangle = q = p Ć q = pq
(ii) Length = 10m
Breadth = 5n
ā“ Area = 10m Ć 5n
= 10 Ć 5 Ć m Ć n
= 50 mn
(iii) Length = 20x2
Breadth = 5y2
ā“ Area = 20x2 Ć 5y2
= 20 Ć 5 Ć x2 Ć y2
= 100x2y2
(iv) Length = 4x
Breadth = 3x2
ā“ Area = 4x Ć 3 Ć x2
= 4 Ć 3 Ć x Ć x2 = 12x3
(v) Length = 3mn
Breadth = 4np
ā“ Area = 3mn Ć 4np
= (3 Ć 4) Ć m Ć n Ć n Ć p = 12 mn2p
Question 3.
Complete the table of products?
Solution:
2x Ć (-5y) = [2 Ć (-5)] Ć x Ć y = -10xy
2x Ć 3x2 = (2 Ć 3) Ć x Ć x2 = 6x3
2x Ć (-4xy) = [2 Ć (-4)] Ć x Ć xy = -8x2y
2x Ć 7x2y = (2 Ć 7) Ć x Ć x2y = 14x3y
2x Ć (-9x2y2) = [2 Ć (-9)] Ć x Ć x2y2 = -18x3y2
-5y Ć 2x = [-5 Ć 2] Ć y Ć x = -10xy
-5y Ć (-5y) = [-5 Ć 5)] Ć y Ć y = 25y2
-5y Ć 3x2 = (-5 Ć 3) Ć y Ć x2 = -15x2y
-5y Ć (-4xy) = [-5 Ć (-4)] Ć y Ć xy = 20 x2y
-5y Ć 7x2y = [-5 Ć 7] Ć y Ć x2y = -35x2y2
-5y Ć (-9x2y2) = [-5 Ć (-9)] Ć y Ć x2y2 = 45x2y3
3x2Ā Ć 2x = [3 Ć 2] Ć x2 Ć x = 6x3
3x2 Ć (-5y) = [3 Ć (-5)] Ć x2 Ć y = -15x2y
3x2 Ć 3x2 = [3 Ć 3] Ć x2 Ć x2 = 9x4
3x2 Ć (-4xy) = [3 Ć (-4)] Ć x2 Ć xy = -12x3y
3x2 Ć 7x2y = [3 Ć 7] Ć x2 Ć x2y
3x2 Ć (-9x2y2) = [3 Ć (-9)] Ć x2 Ć x2y2 = -27x4y2
– 4xy Ć 2x = [-4 Ć 2] Ć xy Ć x = -8x2y
– 4xy Ć (-5y) = [-4 Ć (-5)] Ć xy Ć y = 20xy2
– 4xy Ć 3x2 = [-4 Ć 3] Ć xy Ć x2 = -12x3y
– 4xy Ć 7x2y = [-4 Ć 7] Ć xy Ć x2y = -28x3y2
– 4xy Ć (-9x2y2) = [-4 Ć (-9)] Ć xy Ć x2y2 = 36x3y3
7x2y Ć 2x = [7 Ć 2] Ć x2y Ć x = 14x3y
7x2y Ć (-5y) = [7 Ć (-5)] Ć x2y Ć x = 14x3y
7x2y Ć (-5y) = [7 Ć (-5)] Ć x2y Ć y = -35x2y2
7x2y Ć 3x2 = [7 Ć 3] Ć x2y Ć x2 = 21x4y
7x2y Ć (-4xy) = [7 Ć (-4)] Ć x2y Ć xy = -28x3y2
7x2y Ć 7x2y = [7 Ć 7] Ć x2y Ć x2y = 49x4y2
7x2y Ć -9x2y2 = [7 Ć (-9)] Ć x2y Ć x2y = -63x4y3
– 9x2y2 Ć 2x = [-9 Ć 2] Ć x2y2 Ć x = -18x3y2
– 9x2y2 Ć (-5y) = [-9 Ć (-5)] Ć x2y2 Ć y = 45x2y3
– 9x2y2 Ć 3x2 = [-9 Ć 3] Ć x2y2 Ć x2 = -27x4y2
– 9x2y2 Ć (-4xy) = [-9 Ć (-4)] Ć x2y2 Ć xy = 36x3y3
– 9x2y2 Ć 7x2y = [-9 Ć 7] Ć x2y2 Ć x2y = -63x4y3
– 9x2y2 Ć (- 9x2y2) = [-9 Ć (-9)] Ć x2y2 Ć x2y2 = 81x4y4
Question 4.
Obtain the volume of rectangular boxes with the following length, breadth, height respectively?
- 5a, 3a2, 7a4
- 2p, 4q, 8r
- xy, 2x2y, 2xy2
- a, 2b, 3c
Solution:
Volume of the rectangular box
= Length Ć Breadth Ć Height
1. Length = 5a; Breadth = 3a2, Height
= 5a Ć 3a2 Ć 7a4
= (5 Ć 3 Ć 7) Ć a Ć a2 Ć a4
= 105 Ć a7 = 105a7
2. Length = 2p, Breadth = 4q, Height = 8r
ā“ Volume = Length Ć Breadth Ć Height
= 2p Ć 4q Ć 8r
= (2 Ć 4 Ć 8) Ć p Ć q Ć r
= 64 Ć pqr = 64pqr
3. Length = xy, Breadth = 2x2y, Height = 2xy2
ā“ Volume = Length Ć Breadth Ć Height
= xy + 2x2y Ć 2xy2
= (1 Ć 2 Ć 2) Ć xy Ć x2y Ć x2y
= 4 Ć x4y4 = 4x4y4
4. Length = a, Breadth = 2b, Height = 3c
ā“ Volume = Length Ć Breadth Ć Height
= a Ć 2b Ć 3c
= (1 Ć 2 Ć 3) Ć a Ć b Ć c
= 6 Ć abc = 6abc
Question 5.
obtain the product of
- xy, yz, zx
- a, a -a2, a2
- 2, 4y, 8y2, 16y3
- a, 2b, 3c, 6abc
- m, -mn, mnp
Solution:
1. xy Ć yz Ć zx = (1 Ć 1 Ć 1) Ć x Ć y Ć y Ć z Ć z Ć x = 1 Ć (x2 Ć y2 Ć z2) = x2y2z2
2. a Ć (-a)2 Ć a3 = [1 Ć (-1) Ć 1] Ć a Ć a2 Ć a3
= (-1) Ć a6 = -a6
3. 2 Ć 4y Ć 8y2 Ć 16y3
= (2 Ć 4 Ć 8 Ć 16) Ć y Ć y2 Ć y3
= 1024 Ć y6 = 1024y6
4. a Ć 2b Ć 3c Ć 6abc
= (1 Ć 2 Ć 3 Ć 6) Ć a Ć b Ć c Ć abc
= 36 Ć a2b2c2 = 36a2b2c2
5. m Ć (-mn) Ć mnp = [1 Ć (-1) Ć 1] Ć m Ć mn Ć mnp = (-1)m2n2p = -m3n2p