9. Algebraic Expressions and Identities – Class 8 Mathematics NCERT Chapter 9 Complete Guide (CBSE)
NCERT Class 8 Mathematics Chapter 9: Algebraic Expressions and Identities – All Exercise Solutions | CBSE Board
Chapter 9: Algebraic Expressions and Identities
Exercise 9.1
1. Identify the terms, their coefficients for each of the following expressions.
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
Solution: We have ,
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Terms |
Coefficients |
|
(i) |
|
5 3 |
|
(ii) |
1 |
1 1 1 |
|
(iii) |
|
4 – 4 1 |
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(iv) |
3 |
3 – 1 1 – 1 |
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(v) |
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– 1 |
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(vi) |
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0.3 – 0.6 0.5 |
2. Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories?
, 1000 , 
, 
, 
, 
, 
, 
, 
, 
, 
,
Solution: We have ,
|
Monomials |
Binomials |
Trinomials |
|
1000 , |
|
|
,
, 
,
,
,The polynomials that do not fit in these categories : 
and 
3. Add the following.
(i) 
(ii) 
(iii) 
(iv) 
Solution: (i)
We have ,
(ii)
We have ,
(iii) 
We have ,
(iv) 
We have ,
4. (a) Subtract : 
from 
(b) Subtract : 
from 
(c) Subtract : 
from 
.
Solution: (a) Subtract : from
(b) Subtract : from
Now,
Solution: (c) Subtract : 
from 
.
Now ,
Exercise 9.2
1. Find the product of the following pairs of monomials.
(i) 
(ii) 
(iii) 
(iv) 
(v) 
Solution: (i) 
We have, 
(ii) 
We have , 
(iii) 
We have , 
(iv) 
We have, 
(v) 
We have, 
2. Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively.
; 
; 
; 
; 
Solution: (i)
Here , length 
, breadth 
We know that , Area of rectangle = length × breadth 
(ii) 
Here , length 
, breadth 
We know that , Area of rectangle = length × breadth 
(iii)
Here , length 
, breadth 
We know that , Area of rectangle = length × breadth 
(iv)
Here , length 
, breadth 
We know that , Area of rectangle = length × breadth 
(v)
Here , length 
, breadth 
We know that , Area of rectangle = length × breadth 
3. Complete the table of products.
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First monomial Second monomial |
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...... |
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....... |
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....... |
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...... |
Solution: We have ,
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First monomial Second monomial |
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4. Obtain the volume of rectangular boxes with the following length, breadth and height respectively.
(i) 
(ii) 
(iii) 
(iv) 
Solution: (i) Here, Length 
, Breadth 
and Height 
We know that , the volume of rectangular boxes = length × breadth × height
(ii)
Here, Length 
, Breadth 
and Height
We know that , the volume of rectangular boxes = length × breadth × height
(iii) 
Here, Length 
, Breadth 
and Height 
We know that , The volume of rectangular boxes = length × breadth × height
(iv)
Here, Length 
, Breadth 
and Height 
We know that , the volume of rectangular boxes = length × breadth × height
We have, 
5. Obtain the product of
(i) 
(ii) 
(iii) 
(iv) 
(v) 
Solution: (i) 
We have,
(ii) 
We have, 
(iii) 
We have, 
(iv)
We have , 
(v)
We have, 
Exercise 9.3
1. Carry out the multiplication of the expressions in each of the following pairs.
(i) 
(ii) 
(iii) 
(iv) 
(v) 
Solution: (i) 
We have , 
(ii) 
We have, 
(iii) 
We have , 
(iv) 
We have, 
(v)
We have , 
2. Complete the table :
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First expression |
Second expression |
Product |
|
(i) (ii) (iii) (iv) (v) |
|
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…….. ……. ……. …… ……. |
Solution: (i) We have , 
(ii) We have, 
(iii) We have, 
(iv) We have, 
(v) We have, 
3. Find the product .
(i) 
(ii) 
(iii) 
(iv)
Solution: (i)
We have , 
(ii)
We have , 
(iii)
We have, 
(iv)
We have, 
4. (a) Simplify 
and find its values for (i) 
(ii) 
(b) Simplify 
and find its value for (i) 
, (ii) 
(iii) 
.
Solution: (a) We have, 
(i) 
So, 
(ii)
So, 
5. (a) Add: 
and 
(b) Add: 
and 
(c) Subtract: 
from 
(d) Subtract: 
from 
.
Solution: (a) Add: 
and 
.
We have, 
Now ,
(b) Add: 
and 
We have, 
and 
Now ,
(c) Subtract: from
We have, 
and 
Now ,
(d) Subtract: 
from 
.
We have, 
and 
Now ,
Exercise 9.4
1. Multiply the binomials.
(i) 
and 
(ii) 
and 
(iii) 
and 
(iv) 
and 
(v) 
and 
(vi) 
and 
Solution: (i) and
We have, 
(ii) and
We have, 
(iii) and
We have, 
(iv) and
We have, 
(v) and
We have, 
(vi) and
We have, 
2. Find the product.
(i) 
(ii) 
(iii) 
(iv) 
Solution: (i)
We have, 
(ii)
We have, 
(iii)
We have, 
(iv)
We have, 
3. Simplify.
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
(vii) 
(viii) 
Solution: (i) We have, 
(ii) We have, 
(iii) We have, 
(iv) We have, 
(v) We have, 
(vi) We have, 
(vii) We have, 
(viii) We have, 
Exercise 9.5
|
Standard Identities : 1. 2. 3. 4. |
1. Use a suitable identity to get each of the following products.
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
(vii) 
(viii) 
(ix) 
(x) 
Solution: (i) We have, 
(ii) We have, 
(iii) We have, 
(iv) We have, 
(v) We have, 
(vi) We have, 
(vii) We have, 
(viii) We have, 
(ix) We have, 
(x) We have, 
2. Use the identity 
to find the following products.
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
(vii) 
Solution: (i) We have, 
(ii) We have, 
(iii) We have, 
(iv) We have, 
(v) We have, 
(vi) We have, 
(vii) We have, 
3. Find the following squares by using the identities.
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
Solution: (i) We have, 
(ii) We have, 
(iii) We have, 
(iv) We have, 
(v) We have, 
(vi)We have, 
4. Simplify.
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
(vii) 
Solution: (i) We have, 
(ii)We have, 
(iii) We have, 
(iv) We have, 
(v) We have,
(vi)We have, 
(vii) We have , 
5. Show that.
(i) 
(ii) 
(iii) 
(iv) 
(v) 
Solution: (i) 
LHS : 
RHS
(ii) 
LHS : 
RHS
(iii)
LHS: 
RHS
(iv) 
LHS: 
RHS
(v) 
LHS : 
RHS
6. Using identities, evaluate.
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 297 × 303 (vii) 78 × 82 (viii) 
(ix) 10.5 × 9.5
Solution: (i) We have, 
(ii) We have, 
(iii) We have, 
(iv) We have, 
(v) We have, 
(vi) We have, 
(vii) We have, 
(viii) We have, 
(ix) We have, 
7. Using 
, find
(i) 
(ii) 
(iii) 
(iv) 
Solution: (i) We have, 
(ii) We have, 
(iii) We have, 
(iv) We have, 
8. Using 
, find
(i) 103 × 104 (ii) 5.1 × 5.2 (iii) 103 × 98 (iv) 9.7 × 9.8
Solution: (i) We have, 
(ii) We have, 
(iii) We have, 
(iv) We have, 
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