8th Maths 9.2

Chapter 9

Algebraic Expressions and Identities

NCERT Class 8th solution of Exercise 9.1 

NCERT Class 8th solution of Exercise 9.3

NCERT Class 8th solution of Exercise 9.4

NCERT Class 8th solution of Exercise 9.5

Exercise 9.2

Q1. Find the product of the following pairs of monomials.

i) `4, 7p`

ii) `-4p, 7p`

iii) `-4p, 7pq`

iv) `4p^3, -3p`

v) `4p, 0`

`text{Sol.}`

i) `4times 7p``= 28p`

ii) `-4ptimes 7q``= -28p^2`

iii) `-4ptimes 7pq``= -28p^2q`

iv) `4p^3times -3p``= -12p^4`

v) `4ptimes 0``= 0`

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

`(p, q);` 

`(10m, 5n);` 

`(20x^2, 5y^2);`

`(4x, 3x^2);` 

`(3mn, 4np)`

`text{Sol.}`

i) `text{The length }p text{ and breadth }q text{ units}`

`text{Area of rectangles = length}times text{breadth}`

`= p times q`

`= pq text{ square units}`

`text{Answer:}`

`= pq text{ square units}`

ii)  `text{The length }10m text{ and breadth }5ntext{ units}`

`text{Area of rectangles = length}times text{breadth}`

`= 10m times 5n`

`= 50 text{ square units}`

`text{Answer:}`

`= 50 text{ square units}`

iii) `text{The length }20x^2 text{ and breadth }5y^2 text{ units}`

`text{Area of rectangles = length}times text{breadth}`

`= 20x^2 times 5y^2`

`= 100x^2y^2 text{ square units}`

`text{Answer:}`

`= 100x^2y^2 text{ square units}`

iv) `text{The length }4x text{ and breadth } 3x^2text{ units}`

`text{Area of rectangles = length}times text{breadth}`

`= 4x times 3x^2`

`= 12x^3 text{ square units}`

`text{Answer:}`

`= 12x^3 text{ square units}`

v) `text{The length }3mn text{ and breadth }4np text{ units}`

`text{Area of rectangles = length}times text{breadth}`

`= 3mn times 4np`

`= 12mn^2 text{ square units}`

`text{Answer:}`

`= 12mn^2 text{ square units}`

Q3. Complete the table of products.

`text{Answer:}`

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

i) `5a, 3a^2, 7a^4`

ii) `2p, 4q, 8r`

iii) `xy, 2x^2y, 2xy^2`

iv) `a, 2b, 3c`

`text{Sol.}`

i) `text{The length }5a text{ breadth }3a^2``text{ and height }7a^4 text{ units}`

`text{Vol. of rectangles = length}times text{breadth}times text{height}`

`= 5a times 3a^2 times 7a^4`

`= 105a^7 text{ cube units}`

`text{Answer:}`

`= 105^7 text{ cube units}`

ii) `text{The length }2p text{ breadth }4q``text{ and height }8r text{ units}`

`text{Vol. of rectangles = length}times text{breadth}times text{height}`

`= 2p times 4q times 8r`

`= 64pqr text{ cube units}`

`text{Answer:}`

`= 64pqr text{ cube units}`

iii) `text{The length }xy text{ breadth }2x^2y``text{ and height }2xy^2text{ units}`

`text{Vol. of rectangles = length}times text{breadth}times text {height}`

`= xy times 2x^2y times 2xy^2`

`= 4x^4y^4 text{ cube units}`

`text{Answer:}`

`= 4x^4y^4 text{ cube units}`

iv) `text{The length }a text{ breadth }2b``text{ and height }3c text{ units}`

`text{Vol. of rectangles = length}times text{breadth}times text{height}`

`= a times 2b times 3c`

`= 6abc text{ cube units}`

`text{Answer:}`

`= 6abc text{ cube units}`

Q5. Obtain the product of

i) `xy, yz, zx`

ii) `a, -a^2, a^3`

iii) `2, 4y, 8y^2, 16y^3`

iv)  `a, 2b, 3c, 6abc`

v) `m, -mn, mnp`

`text{sol.}`

i) `xy times yz times zx`

`= x^2y^2z^2`

`text{Answer:}`

`=x^2y^2z^2`

ii) `atimes( -a)^2times a^3`

`= atimesa^2timesa^3`

`= a^6`

`text{Answer:}`

`= a^6`

iii) `2times 4y times 8y^2 times 16y^3`

`= 1024y^6`

`text{Answer:}`

`= 1024y^6`

iv)  `atimes 2b times 3ctimes 6abc`

`= 36a^3b^2c^2`

`text{Answer:}`

`= 36a^3b^2c^2`

v) `m times (-mn)times mnp`

`= -m^3n^2p`

`text{Answer:}`

`= -m^3n^2p`