Contents

- 1 NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities
- 1.1 Chapter 9 Algebraic Expressions and Identities Exercise 9.1
- 1.2 Chapter 9 Algebraic Expressions and Identities Exercise 9.2
- 1.3 Chapter 9 Algebraic Expressions and Identities Exercise 9.3
- 1.4 Chapter 9 Algebraic Expressions and Identities Exercise 9.4
- 1.5 Chapter 9 Algebraic Expressions and Identities Exercise 9.5

NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities.

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 8 |

Subject |
Maths |

Chapter |
Chapter 9 |

Chapter Name |
Algebraic Expressions and Identities |

Exercise |
Ex 9.1, Ex 9.2, Ex 9.3, Ex 9.4, Ex 9.5 |

Number of Questions Solved |
25 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities

### Chapter 9 Algebraic Expressions and Identities Exercise 9.1

**Question 1.**

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

**(i)** 5xyz^{2} – 3zy

**(ii)** 1 + x + x^{2}

**(iii)** 4x^{2}y^{2} – 4x^{2}y^{2}z^{2} + z^{2}

**(iv)** 3 – pq + qr -rp

**(v)**

**(vi)** 0.3a – 0.6ab + 0.5b

**Solution:**

**(i)** In the expression 5xyz^{2} – 3zy, the terms are 5xyz^{2} and -3zy.

Coefficient of xyz^{2} in the term 5xyz^{2} is 5.

Coefficient of zy in the term – 3yz is – 3.

**(ii)** In the expression 1 + x + x^{2}, the terms are 1, x and x^{2}.

Coefficient of term 1 is 1.

Coefficient of x in the term x is 1.

Coefficient of x^{2} in the term x^{2} is 1.

**(iii)** In the expression 4x y – 4xyz + z , the terms are 4x^{2}y^{2}, – 4x^{2}y^{2}z^{2} and z^{2}.

Coefficient of x^{2}y^{2} in the term 4x^{2}y^{2} is 4.

Coefficient of x^{2}y^{2}z^{2} in the term – 4x^{2}y^{2}z^{2} is – 4.

Coefficient of z^{2} in the term z2 is 1.

**(iv)** In the expression 3 – pq + qr – rp, the terms are 3, – pq, qr and – rp.

Coefficient of term 3 is 3.

Coefficient of pq in the term – pq is -1.

Coefficient of qr in the term qr is 1.

Coefficient of rp in the term – rp is -1.

**(v)** In the expression , the terms are and – xy.

Coefficient of x in the term is

Coefficient of y in the term is

Coefficient of xy in the term – xy is -1.

**(vi)** In the expression 0.3a -0.6 ab + 0.5 b, the terms are 0.3a, – 006ab and 0.5b.

Coefficient of a in the term 0.3a is 0.3.

Coefficient of ab in the term – 0.6ab is – 0.6.

Coefficient of b in the term 0.5b is 0.5.

**Question 2.**

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

x + y, 1000, x + x^{2} + x^{3} + x^{4}, 7 + y + 5x, 2y – 3y^{2}, 2y – 3y^{2} + 4y^{3}, 5x – 4y + 3xy, 4z – 15z2, ab + bc+cd + da, pqr, p^{2}q + pq^{2}, 2p + 2q.

**Solution:**

The given polynomials are classified as under :

Monomials : 1000, pqr

Binomials : x + y, 2y – 3y^{2}, 4z -15z^{2}, p^{2}q + pq^{2}, 2p + 2q.

Trinomials : 7 + y + 5x, 2y – 3y^{2} + 4y^{3}, 5x – 4y + 3x.

Polynomials that do not fit in any categories :

x + x^{2} + x^{3} + x^{4}, ab + be + cd + da.

**Question 3.**

Add the following :

**(i)** ab – be, be – ca, ea – ab

(ii) a – b + ab, b-c + be, c – a + ac

**(iii)** 2p^{2}q^{2} – 3pq + 4, 5 + 7pq – 3p^{2}q^{2}

**(iv)** l^{2} + m^{2}, m^{2} + n^{2}, n^{2} + l^{2}, 2Im + 2mn + 2nl

**Solution:**

**(i)** Writing the given expressions in separate rows with like terms one below the other, we have

**(ii)** Writing the given expressions in separate rows with like terms one below the other, we have

**(iii)** Writing the given expressions in separate rows with like terms one below the other, we have

**(iv)** Writing the given expressions in separate rows with like terms one below the other, we have

**Question 4.**

**(a)** Subtract

4a – lab +36 + 12 from 12a – 9a6 + 56-3

**(b)** Subtract

3xy + 5yz – Izx from 5xy – 2yz – 2zx + IQxyz

**(c)** Subtract 4p^{2}q – 3pq + 5pq^{2} – 8p + 7q – 10 from 18 – 3p – 11q + 5pq – 2pq^{2} + 5p^{2}q.

**Solution:**

Rearranging the terms of the given expressions, changing the sign of each term of the expression to be subtracted and adding the two expressions, we get

### Chapter 9 Algebraic Expressions and Identities Exercise 9.2

**Question 1.**

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

**Solution:**

**(i)** 4 x 7p = (4 x 7) x p = 28p

**(ii)** – 4 p x 7p = (- 4 x 7) x (px P)

= -28p^{1} + ^{1} = – 28p^{2}

**(iii)** -4px 7pq = (- 4 x 7) x (p x p x q)

= -28 p^{1+1}q = – 28p^{2}q

**(iv)** 4p^{3} x – 3p = (4 x – 3) x (p^{3} x p)

= – 12p^{3+1} = =-12p^{4}

**(v)** 4p x 0 = (4 x 0) x p = 0 x p = 0

**Question 2.**

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)

**Solution:**

We know that the area of a rectangle = l x b, where l = length and b = breadth.

Therefore, the areas of rectangles with pair of monomials (p, q); (10m, 5n); (20x^{2}, 5y^{2}); (4x, 3x^{2}) and (3mn, 4np) as their lengths and breadths are given by

pxq=pq

10 m x 5n = (10 x 5) x (m x n) = 50 mn

20x^{2} x 5y^{2} = (20 x 5) x (x^{2} x y^{2}) = 100x^{2}y^{2}

4x x 3x^{2} = (4 x 3) x (x x x^{2})

= 12x^{2}

and, 3 mn x 4np = (3×4 )x(mxnxnxp)

=12 mn^{2}p

**Question 3.**

Complete the table of products :

**Solution:**

Completed table is as under :

**Question 4.**

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^{2}y, 2xy^{2}

**(iv)** a, 2b, 3c

**Solution:**

**(i)** Required volume = 5a x 3a^{2} x 7a^{4}

= (5 x 3 x 7) x (a x a^{2} x a^{4})

= 105a^{1+2+4} =105a^{7}

**(ii)** Required volume = 2p x 4q x 8r

= (2 x 4 x 8 )x p x q x r = 64 pqr

**(iii)** Required volume =xy x 2x^{2}y x 2xy^{2}

= (1 x 2 x 2) x (x x x^{2} x x x y x y x y^{2})

= 4x^{1+2+1} y^{1+1+2} = 4x^{4}y^{4}

**(iv)** Required volume =a x 2b x 3c

= (1 x 2 x 3) x (a x b x c)

= 6abc

**Question 5.**

Obtain the product of

**(i)** xy, yz, zx

**(ii)** a, – a^{2}, a^{3}

**(iii)** 2, 4y, 8y^{2}, 16y^{3}

**(iv)** a, 26, 3c, 6a6c

**(v)** m, – mn, mnp

**Solution:**

### Chapter 9 Algebraic Expressions and Identities Exercise 9.3

**Question 1.**

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

**(i)** 4p, q r + r

**(ii)** ab, a – -b

**(iii)** a + b, 7a^{2}b^{2}

**(iv)** a^{2}– 9, 4a

**(v)** pq + qr + rp, 0

**Solution:**

**(i)** 4p x (q + r) = 4px q + 4p x r

= 4pq + 4pr

**(ii)** ab x (a – b) = ab x a – ab

= a^{2}b – ab^{2}

**(iii)** (a + b) x 7a^{2}b^{2} = a x 7a^{2}b^{2} + b x 7a^{2}b^{2}

= 7a^{3}b^{2} + 7a^{2}b^{3}

**(iv)** (a^{2} -9)x 4a = a^{2} x 4a – 9 x 4a

= 4a^{3} – 36a

**(v)** (pq + qr + rp) x 0 = 0

**Question 2.**

Complete the table :

**Solution:**

Completed table is as under :

**Question 3.**

Find the product:

**Solution:**

**Question 4.**

**(a)** Simplify : 3x (4x – 5) + 3 and find its value for

**(i)** x = 3,

**(ii)** x =

**(b)** Simplify : a (a^{2} + a + 1) + 5 and find its value for

**(i)** a = 0,

**(ii)** a = 1,

**(iii)** a = – 1

**Solution:**

**Question 5.**

**(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 : 31 (l – 4m + 5n) from 41 (lOn – 3m + 21)

**(d)** Subtract : 3a (a + b + c) – 2b (a – 6 + c) from 4c (-a + b + c)

**Solution:**

### Chapter 9 Algebraic Expressions and Identities Exercise 9.4

**Question 1.**

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 + 3q^{2}) and (3pq – 2q^{2})

**(vi)**

**Solution:**

**Question 2.**

Find the product :

**(i)** (5 – 2x)(3 + x)

**(ii)** (x + 7y)(7x – y)

**(iii)** (a^{2} + b)(a + b^{2} )

**(iv)** (p^{2} – q^{2})(2p + q)

**Solution:**

**Question 3.**

Simplify :

**(i)** (x^{2} – 5)(x + 5) + 25

**(ii)** (a^{2} +5)(b^{3} +3)+ 5

**(iii)** (t +s^{2})(^{2} – 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)(x^{2} – xy + y^{2})

**(vii)** (1.5x – 4y) (1.5x + 4y + 3) – 4.5x + 12y

**(viii)** (a + b + c)(a + b – c)

**Solution:**

### Chapter 9 Algebraic Expressions and Identities Exercise 9.5

**Question 1.**

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) (1.1m + 0.4)

**(vi)** (a^{2} + b^{2}) (- a^{2} + b^{2})

**(vii)** (6x – 7) (6x + 7)

**(viii)** (- a + c) (- a + c)

**(ix)**

**(x)** (7a – 9b)(7a – 9b)

**Solution:**

**Question 2.**

Use the identity (x + a) (x + b) = x^{2} + (a + b)x + ab to find the following products.

**(i)** (x + 3) (x + 7)

**(ii)** (4x + 5) (4x + 1)

**(iii)** (4^{2} – 5) (4x – 1)

**(iv)** (4x + 5) (4^{2} – 1)

**(v)** (2x + 5y) (2x + 3y)

**(vi)** (2a^{2} + 9) (2a^{2} + 5)

**(vii)** (xyz – 4) (xyz – 2)

**Solution:**

**Question 3.**

Find the following squares by using the identities :

**(i)** (b – 7)^{2}

**(ii)** (xy + 3z)^{2}

**(iii)** (6x^{2} – 5y^{2})

**(iv)**

**(v)** (0.4p – 0.5q)^{2}

**(vi)** (2xy + 5y)^{2}

**Solution:**

**Question 4.**

Simplify :

**(i)** (a^{2} – b^{2})^{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} – 2ab^{2}c

**(vii)** (m^{2} – n^{2}m)^{2} + 2m^{3}n^{2}

**Solution:**

**Question 5.**

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} = 48pq^{2}

**(v)** (a – b)(a + b) + (b – c)(b + c) + (c – a)(c + a) = 0

**Solution:**

**Question 6.**

Using identities, evaluate : .

**(i)** 71^{2}

**(ii)** 99^{2}

**(iii)** 102^{2}

**(iv)** 998^{2}

**(v)** 5.2^{2}

**(vi)** 297 x 303

**(vii)** 78 x 82

**(viii)** 8.9^{2}

**(ix)** 1.05 x 9.5

**Solution:**

**Question 7.**

Using a^{2} – b^{2} = (a + b) (a – b), find

**(i)** 51^{2} – 49^{2}

**(ii)** (1.02)^{2} – (0.98)^{2}

**(iii) **153^{2} – 147^{2}

**(iv)** 12.1^{2} – 7.9^{2}

**Solution:**

**Question 8.**

Using (x + a) (x + b) = x + (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

**Solution:**

We hope the NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities, drop a comment below and we will get back to you at the earliest.

## Leave a Reply