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
- 4p
^{3}, -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 = -28p^{2}

3. -4p and 7pq

-4p Ć 7pq = (-4 Ć 7) Ć p Ć pq = -28 Ć p^{2}q = -28p^{2}q

4. 4p^{3} and -3p

4p^{3} Ć (-3p) = (4 Ć (-3)}p^{3} Ć p = -12 Ć p^{4}

= -12p^{4}

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); (20x^{2}, 5y^{2}); (4x, 3x^{2}); (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 = 20x^{2}

Breadth = 5y^{2}

ā“ Area = 20x^{2} Ć 5y^{2}

= 20 Ć 5 Ć x^{2} Ć y^{2}

= 100x^{2}y^{2}

(iv) Length = 4x

Breadth = 3x^{2}

ā“ Area = 4x Ć 3 Ć x^{2}

= 4 Ć 3 Ć x Ć x^{2} = 12x^{3}

(v) Length = 3mn

Breadth = 4np

ā“ Area = 3mn Ć 4np

= (3 Ć 4) Ć m Ć n Ć n Ć p = 12 mn^{2}p

Question 3.

Complete the table of products?

Solution:

2x Ć (-5y) = [2 Ć (-5)] Ć x Ć y = -10xy

2x Ć 3x^{2} = (2 Ć 3) Ć x Ć x^{2} = 6x^{3
}2x Ć (-4xy) = [2 Ć (-4)] Ć x Ć xy = -8x^{2}y

2x Ć 7x^{2}y = (2 Ć 7) Ć x Ć x^{2}y = 14x^{3}y

2x Ć (-9x^{2}y^{2}) = [2 Ć (-9)] Ć x Ć x^{2}y^{2} = -18x^{3}y^{2
}-5y Ć 2x = [-5 Ć 2] Ć y Ć x = -10xy

-5y Ć (-5y) = [-5 Ć 5)] Ć y Ć y = 25y^{2}

-5y Ć 3x^{2} = (-5 Ć 3) Ć y Ć x^{2} = -15x^{2}y

-5y Ć (-4xy) = [-5 Ć (-4)] Ć y Ć xy = 20 x^{2}y

-5y Ć 7x^{2}y = [-5 Ć 7] Ć y Ć x^{2}y = -35x^{2}y^{2}

-5y Ć (-9x^{2}y^{2}) = [-5 Ć (-9)] Ć y Ć x^{2}y^{2} = 45x^{2}y^{3}

3x^{2}Ā Ć 2x = [3 Ć 2] Ć x^{2} Ć x = 6x^{3}

3x^{2} Ć (-5y) = [3 Ć (-5)] Ć x^{2} Ć y = -15x^{2}y

3x^{2} Ć 3x^{2} = [3 Ć 3] Ć x^{2} Ć x^{2} = 9x^{4}

3x^{2} Ć (-4xy) = [3 Ć (-4)] Ć x^{2} Ć xy = -12x^{3}y

3x^{2} Ć 7x^{2}y = [3 Ć 7] Ć x^{2} Ć x^{2}y

3x^{2} Ć (-9x^{2}y^{2}) = [3 Ć (-9)] Ć x^{2} Ć x^{2}y^{2} = -27x^{4}y^{2}

– 4xy Ć 2x = [-4 Ć 2] Ć xy Ć x = -8x^{2}y

– 4xy Ć (-5y) = [-4 Ć (-5)] Ć xy Ć y = 20xy^{2}

– 4xy Ć 3x^{2} = [-4 Ć 3] Ć xy Ć x^{2} = -12x^{3}y

– 4xy Ć 7x^{2}y = [-4 Ć 7] Ć xy Ć x^{2}y = -28x^{3}y^{2}

– 4xy Ć (-9x^{2}y^{2}) = [-4 Ć (-9)] Ć xy Ć x^{2}y^{2} = 36x^{3}y^{3
}7x^{2}y Ć 2x = [7 Ć 2] Ć x^{2}y Ć x = 14x^{3}y

7x^{2}y Ć (-5y) = [7 Ć (-5)] Ć x^{2}y Ć x = 14x^{3}y

7x^{2}y Ć (-5y) = [7 Ć (-5)] Ć x^{2}y Ć y = -35x^{2}y^{2}

7x^{2}y Ć 3x^{2} = [7 Ć 3] Ć x^{2}y Ć x^{2} = 21x^{4}y

7x^{2}y Ć (-4xy) = [7 Ć (-4)] Ć x^{2}y Ć xy = -28x^{3}y^{2}

7x^{2}y Ć 7x^{2}y = [7 Ć 7] Ć x^{2}y Ć x^{2}y = 49x^{4}y^{2}

7x^{2}y Ć -9x^{2}y^{2} = [7 Ć (-9)] Ć x^{2}y Ć x^{2}y = -63x^{4}y^{3}

– 9x^{2}y^{2} Ć 2x = [-9 Ć 2] Ć x^{2}y^{2} Ć x = -18x^{3}y^{2}

– 9x^{2}y^{2} Ć (-5y) = [-9 Ć (-5)] Ć x^{2}y^{2} Ć y = 45x^{2}y^{3}

– 9x^{2}y^{2} Ć 3x^{2} = [-9 Ć 3] Ć x^{2}y^{2} Ć x^{2} = -27x^{4}y^{2}

– 9x^{2}y^{2} Ć (-4xy) = [-9 Ć (-4)] Ć x^{2}y^{2} Ć xy = 36x^{3}y^{3}

– 9x^{2}y^{2} Ć 7x^{2}y = [-9 Ć 7] Ć x^{2}y^{2} Ć x^{2}y = -63x^{4}y^{3}

– 9x^{2}y^{2} Ć (- 9x^{2}y^{2}) = [-9 Ć (-9)] Ć x^{2}y^{2} Ć x^{2}y^{2} = 81x^{4}y^{4}

Question 4.

Obtain the volume of rectangular boxes with the following length, breadth, height respectively?

- 5a, 3a
^{2}, 7a^{4} - 2p, 4q, 8r
- xy, 2x
^{2}y, 2xy^{2} - a, 2b, 3c

Solution:

Volume of the rectangular box

= Length Ć Breadth Ć Height

1. Length = 5a; Breadth = 3a^{2}, Height

= 5a Ć 3a^{2} Ć 7a^{4}

= (5 Ć 3 Ć 7) Ć a Ć a^{2} Ć a^{4}

= 105 Ć a^{7} = 105a^{7}

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 = 2x^{2}y, Height = 2xy^{2}

ā“ Volume = Length Ć Breadth Ć Height

= xy + 2x^{2}y Ć 2xy^{2}

= (1 Ć 2 Ć 2) Ć xy Ć x^{2}y Ć x^{2}y

= 4 Ć x^{4}y^{4} = 4x^{4}y^{4}

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 -a
^{2}, a^{2} - 2, 4y, 8y
^{2}, 16y^{3} - 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 (x^{2} Ć y^{2} Ć z^{2}) = x^{2}y^{2}z^{2}

2. a Ć (-a)^{2} Ć a^{3} = [1 Ć (-1) Ć 1] Ć a Ć a^{2} Ć a^{3}

= (-1) Ć a^{6} = -a^{6}

3. 2 Ć 4y Ć 8y^{2} Ć 16y^{3}

= (2 Ć 4 Ć 8 Ć 16) Ć y Ć y^{2} Ć y^{3}

= 1024 Ć y^{6} = 1024y^{6}

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 a^{2}b^{2}c^{2} = 36a^{2}b^{2}c^{2}

5. m Ć (-mn) Ć mnp = [1 Ć (-1) Ć 1] Ć m Ć mn Ć mnp = (-1)m^{2}n^{2}p = -m^{3}n^{2}p