Class 8 - Maths - Algebraic Expressions and Identities (NCERT Ex 9.2 Answers)

Algebraic Expressions and Identities 

(NCERT Ex 9.2 Answers)

Q1: Find the product of following pair of monomials.

(i) 4 , 7p

Answer:

4   ☓   7p = 4  ☓ 7   ☓ p = 28p

(ii) -4p , 7p

Answer:

-4p   ☓   7p = -4 ☓ p ☓ 7  ☓ p = (-4☓7)☓ (p☓ p) = -28p²

(iii) 4p , 7pq

Answer:

-4p  &#9747 7p = -4 ☓ p ☓7  ☓ p  ☓ q = (-4☓ 7)☓ (p☓ p☓ q) = -28p²q

(iv) 4p³ , -3p

Answer:

4p³  ☓  -3p = 4  ☓(-3)   ☓ p ☓ p☓ p☓ p = -12p⁴

(v) 4p , 0

Answer:

4p ☓ 0 = 4☓ p☓ 0 = 0


Q2: Find the areas of rectangles with the following pairs of monomials as their lengths
and breadths respectively.

(p , q);(10m , 5n);(20x² , 5y²);(4x , 3x²);(3mn ,4np)

Answer:

We know that,

Area of rectangle = Length ☓ Breadth

Area of 1^st rectangle = p ☓ q = pq

Area of 2^nd rectangle = 10m ☓ 5n = 10☓ 5 ☓ m ☓ n = 50mn

Area of 3^rd rectangle = 20x² ☓ 5y² = 20☓ 5 ☓ x² ☓ y² = 100x²y²

Area of 4^th rectangle = 4x ☓ 3x² = 4☓3 ☓ x ☓ x² = 12x³

Area of 5^th rectangle = 3mn ☓4np = 3☓ 4 ☓ m ☓ n ☓ n ☓ p = 12mn²p


Q3: Complete the table of products.

First Monomial (⇨) Second Monomial(⇩)

2x

-5y

3x2

-4xy

7x2y

-9x2y2

2x	4x2	...	...	...	...	...
-5y	...	...	-15x2y	...	...	...
3x2	...	...	...	...	...	...
-4xy	...	...	...	...	...	...
7x2y	...	...	...	...	...	...
-9x2y2	...	...	...	...	...	...

Answer:



The table can be completed as follows.

First Monomial (⇨) Second Monomial(⇩)	2x	-5y	3x2	-4xy	7x2y	-9x2y2
2x	4x2	-10xy	6x3	-8x2y	14x3y	-18x3y2
-5y	-10xy	25y2	-15x2y	20xy2	-35x2y2	45x2y3
3x2	6x3	-15x2y	9x4	-12x3y	21x4y	-27x4y2
-4xy	-8x2y	20xy2	-12x3y	16x2y2	-28x3y2	36x3y3
7x2y	14x3y	-35x2y2	21x4y	-28x3y2	49x4y2	-63x4y3
-9x2y2	-18x3y2	45x2y3	-27x4y2	36x3y3	-63x4y3	81x4y4

Q4: Obtain the volume of rectangular boxes with the following length,breadth
and height respectivly.

(i) 5a , 3a² , 7a⁴

(ii) 2p , 4q , 8r

(iii) xy , 2x²y , 2xy²

(iv) a , 2b , 3c

Answer:

We know that,

Volume = Length ☓ Breadth ☓ Height

(i) Volume= 5a ☓ 3a²☓ 7a⁴= 5☓ 3☓ 7☓a☓ a²☓a⁴ = 105a⁷

(ii) Volume=2p☓ 4q ☓ 8r= 2☓ 4☓ 8☓ p☓ q☓ r = 64pqr

(iii) Volume=xy ☓ 2x²y☓ 2xy²= 2☓2☓ xy☓ x²y☓ xy² = 4x⁴y⁴

(iv) Volume= a ☓ 2b ☓ 3c= 2☓ 3☓ a☓ b☓ c = 6abc

Q5: Obtain the product of

(i) xy , yz , zx

Answer:

xy ☓ yz ☓ zx = x²y²z²

(ii) a , -a² , a³

Answer:

a☓ -a²☓ a³= -a^{1 + 2 + 3} = -a⁶

(iii) 2 , 4y , 8y² , 16y³

Answer:

2☓ 4y☓ 8y²☓16y³= 2☓ 4☓ 8☓ 16☓y ☓y²☓y³ = 1024y⁶

(iv) a , 2b , 3c , 6abc

Answer:

a☓ 2b☓ 3c☓ 6abc= 2☓ 3☓ 6☓ a☓ b ☓ c ☓ abc = 36a²b²c²

(v) m , -mn , mnp

Answer:

m ☓ (-mn)☓ mnp= -m³n²p