NCERT Solutions for Class 8 Maths Maths - NCERT Solution Chapter 9

Algebraic Expressions and Identities Class 8

Chapter 9 Algebraic Expressions and Identities Exercise 9.1, 9.2, 9.3, 9.4, 9.5 Solutions

<< Previous Chapter 8 : Comparing Quantities Next Chapter 10 : Visualising Solid Shapes >>

Exercise 9.1 : Solutions of Questions on Page Number : 140

Q1 :  

Identify the terms, their coefficients for each of the following expressions.

(i) 5xyz2 - 3zy

(ii) 1 + x + x2

(iii) 4x2y2 - 4x2y2z2 + z2

(iv) 3 - pq + qr - rp

(v)

(vi) 0.3a - 0.6ab + 0.5b


Answer :

The terms and the respective coefficients of the given expressions are as follows.

-

Terms

Coefficients

(i)

5xyz2

- 3zy

5

- 3

(ii)

1

x

x2

1

1

1

(iii)

4x2y2

- 4x2y2z2

z2

4

- 4

1

(iv)

3

- pq

qr

- rp

3

- 1

1

- 1

(v)

- xy

- 1

(vi)

0.3a

- 0.6ab

0.5b

0.3

- 0.6

0.5

Answer needs Correction? Click Here

Q2 :  

Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories?

x + y, 1000, x + x2 + x3 + x4, 7 + y + 5x, 2y - 3y2, 2y - 3y2 + 4y3, 5x - 4y + 3xy, 4z - 15z2, ab + bc + cd + da, pqr, p2q + pq2, 2p + 2q


Answer :

The given expressions are classified as

Monomials: 1000, pqr

Binomials: x + y, 2y - 3y2, 4z - 15z2, p2q + pq2, 2p + 2q

Trinomials: 7 + y + 5x, 2y - 3y2 + 4y3, 5x - 4y + 3xy

Polynomials that do not fit in any of these categories are

x+ x2+ x3+ x4, ab + bc + cd + da

Answer needs Correction? Click Here

Q3 :  

Add the following.

(i) ab - bc, bc - ca, ca - ab

(ii) a - b + ab, b - c + bc, c - a + ac

(iii) 2p2q2 - 3pq + 4, 5 + 7pq - 3p2q2

(iv) l2 + m2, m2 + n2, n2 + l2, 2lm + 2mn + 2nl


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

(a) Subtract 4a - 7ab + 3b + 12 from 12a - 9ab + 5b - 3

(b) Subtract 3xy + 5yz - 7zx from 5xy - 2yz - 2zx + 10xyz

(c) Subtract 4p2q - 3pq + 5pq2 - 8p + 7q - 10 from 18 - 3p - 11q + 5pq - 2pq2 + 5p2q


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 8 : Comparing Quantities Next Chapter 10 : Visualising Solid Shapes >>

Exercise 9.2 : Solutions of Questions on Page Number : 143

Q1 :  

Find the product of the following pairs of monomials.

(i) 4, 7p (ii) - 4p, 7p (iii) - 4p, 7pq

(iv) 4p3, - 3p (v) 4p, 0


Answer :

Please Register/Login to get access to all solutions Facebook Login
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 :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  

Complete the table of products.

2x

- 5y

3x2

- 4xy

7x2y

- 9x2y2

2x

4x2

- 5y

- 15x2y

3x2

- 4


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

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

(i) 5a, 3a2, 7a4 (ii) 2p, 4q, 8r (iii) xy, 2x2y, 2xy2

(iv) a, 2b, 3c


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

Obtain the product of

(i) xy, yz, zx (ii) a, - a2, a3 (iii) 2, 4y, 8y2, 16y3

(iv) a, 2b, 3c, 6abc (v) m, - mn, mnp


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 8 : Comparing Quantities Next Chapter 10 : Visualising Solid Shapes >>

Exercise 9.3 : Solutions of Questions on Page Number : 146

Q1 :  

Carry out the multiplication of the expressions in each of the following pairs.

(i) 4p, q + r (ii) ab, a - b (iii) a + b, 7a2b2

(iv) a2 - 9, 4a (v) pq + qr + rp, 0


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  

Complete the table

---

First expression

Second Expression

Product

(i)

a

b + c + d

-

(ii)

x + y - 5

5 xy

-

(iii)

p

6p2 - 7p + 5

-

(iv)

4p2q2

p2 - q2

-

(v)

a + b + c

abc

-


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  

Find the product.

(i) (a2) × (2a22) × (4a26)

(ii)

(iii)

(iv) x × x2 × x3 × x4


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

(a) Simplify 3x (4x - 5) + 3 and find its values for (i) x = 3, (ii) .

(b) a (a2 + a + 1) + 5 and find its values for (i) a = 0, (ii) a = 1, (iii) a = - 1.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

(a) Add: p (p - q), q (q ­­­- r) and r (r ­- p)

(b) Add: 2x (z - x - y) and 2y (z - y - x)

(c) Subtract: 3l (l - 4m + 5n) from 4l (10n - 3m + 2l)

(d) Subtract: 3a (a + b + c) - 2b (a - b + c) from 4c (- a + b + c)


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 8 : Comparing Quantities Next Chapter 10 : Visualising Solid Shapes >>

Exercise 9.4 : Solutions of Questions on Page Number : 148

Q1 :  

Multiply the binomials.

(i) (2x + 5) and (4x - 3) (ii) (y - 8) and (3y - 4)

(iii) (2.5l - 0.5m) and (2.5l + 0.5m) (iv) (a + 3b) and (x + 5)

(v) (2pq + 3q2) and (3pq - 2q2)

(vi)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  

Find the product.

(i) (5 - 2x) (3 + x) (ii) (x + 7y) (7x - y)

(iii) (a2 + b) (a + b2) (iv) (p2 - q2) (2p + q)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  

Simplify.

(i) (x2 - 5) (x + 5) + 25

(ii) (a2 + 5) (b3 + 3) + 5

(iii) (t + s2) (t2 - s)

(iv) (a + b) (c - d) + (a - b) (c + d) + 2 (ac + bd)

(v) (x + y) (2x + y) + (x + 2y) (x - y)

(vi) (x + y) (x2 - xy + y2)

(vii) (1.5x - 4y) (1.5x + 4y + 3) - 4.5x + 12y

(viii) (a + b + c) (a + b - c)


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 8 : Comparing Quantities Next Chapter 10 : Visualising Solid Shapes >>

Exercise 9.5 : Solutions of Questions on Page Number : 151

Q1 :  

Use a suitable identity to get each of the following products.

(i) (x + 3) (x + 3) (ii) (2y + 5) (2y + 5)

(iii) (2a - 7) (2a - 7) (iv)

(v) (1.1m - 0.4) (1.1 m + 0.4) (vi) (a2 + b2) ( - a2 + b2)

(vii) (6x - 7) (6x + 7) (viii) ( - a + c) ( - a + c)

(ix) (x) (7a - 9b) (7a - 9b)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  

Use the identity (x + a) (x + b) = x2 + (a + b)x + ab to find the following products.

(i) (x + 3) (x + 7) (ii) (4x +5) (4x + 1)

(iii) (4x - 5) (4x - 1) (iv) (4x + 5) (4x - 1)

(v) (2x +5y) (2x + 3y) (vi) (2a2 +9) (2a2 + 5)

(vii) (xyz - 4) (xyz - 2)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  

Find the following squares by suing the identities.

(i) (b - 7)2 (ii) (xy + 3z)2 (iii) (6x2 - 5y)2

(iv) (v) (0.4p - 0.5q)2 (vi) (2xy + 5y)2


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

Simplify.

(i) (a2 - b2)2 (ii) (2x +5)2 - (2x - 5)2

(iii) (7m - 8n)2 + (7m + 8n)2 (iv) (4m + 5n)2 + (5m + 4n)2

(v) (2.5p - 1.5q)2 - (1.5p - 2.5q)2

(vi) (ab + bc)2 - 2ab2c (vii) (m2 - n2m)2 + 2m3n2


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

Show that

(i) (3x + 7)2 - 84x = (3x - 7)2 (ii) (9p - 5q)2 + 180pq = (9p + 5q)2

(iii)

(iv) (4pq + 3q)2 - (4pq - 3q)2 = 48pq2

(v) (a - b) (a + b) + (b - c) (b + c) + (c - a) (c + a) = 0


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

Using identities, evaluate.

(i) 712 (ii) 992 (iii) 1022 (iv) 9982

(v) (5.2)2 (vi) 297 x 303 (vii) 78 x 82

(viii) 8.92 (ix) 1.05 x 9.5


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  

Using a2 - b2 = (a + b) (a - b), find

(i) 512 - 492 (ii) (1.02)2 - (0.98)2 (iii) 1532 - 1472

(iv) 12.12 - 7.92


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  

Using (x + a) (x + b) = x2 + (a + b) x + ab, find

(i) 103 x 104 (ii) 5.1 x 5.2 (iii) 103 x 98 (iv) 9.7 x 9.8


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 8 : Comparing Quantities Next Chapter 10 : Visualising Solid Shapes >>

Maths - NCERT Solution - Maths : CBSE NCERT Exercise Solutions for Class 8th for Algebraic Expressions and Identities ( Exercise 9.1, 9.2, 9.3, 9.4, 9.5 ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.