NCERT Solutions for Class 8 Maths chapter-9 Algebraic Expressions and Identities

NCERT solutions for class 8 maths chapter 9 Algebraic Expressions and Identities is prepared by academic team of Physics Wallah. We have prepared solutions for all exercise with importants questions of chapter 9. Given below is step by step solutions of all questions given in NCERT textbook for chapter-9. Read chapter 9 theory make sure you have gone through the theory part of chapter-9 from NCERT textbook and you have learned the formula of the given chapter. Physics Wallah prepared a detail notes and additional questions for class 8 maths with short notes of all maths formula of class 8 maths. do read these contents before moving to solve the exercise of NCERT chapter 9.

NCERT Solutions for Class 8 Maths Exercise 9.1

Question 1.

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

(i)  Algebraic Expressions and Identities/image001.png    ncert solution

(ii) 1 + x + x²

(iii) Algebraic Expressions and Identities/image003.png   

(iv)3 - pq + qr -rp

(v)ncert solution + ncert solution - xy

(vi) 3 - pq + qr -rp

Solution :

(i) Terms: Algebraic Expressions and Identities/image007.png and ncert solution

Coefficient in Algebraic Expressions and Identities/image007.png is 5 and in ncert solution is  -3

(ii) Terms: 1, x and

Coefficient of Algebraic Expressions and Identities/image007.png and coefficient of x²  is 1.

(iii) Terms: Algebraic Expressions and Identities/image014.png and 

Coefficient in Algebraic Expressions and Identities/image016.pngis 4, coefficient of Algebraic Expressions and Identities/image017.png is -4  and coefficient of is 1.

(iv) Terms: 3, -pq, qr  and -rp

Coefficient of -pq is -1, coefficient of qr is 1 and coefficient of -rp is Algebraic Expressions and Identities/image025.png

(v) Terms: Algebraic Expressions and Identities/image026.png and  -xy

Coefficient of Algebraic Expressions and Identities/image028.png isAlgebraic Expressions and Identities/image029.png coefficient of Algebraic Expressions and Identities/image030.pngis Algebraic Expressions and Identities/image029.png and coefficient of -xy is -1.

(vi) Terms:  0.3a, -0.6ab  and 0.5b

Coefficient of 0.3a  is 0.3, coefficient of -0.6ab  is -0.6 and coefficient of 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:

Algebraic Expressions and Identities/image037.pngAlgebraic Expressions and Identities/image038.png

Solution :

 (i) Since Algebraic Expressions and Identities/image049.png contains two terms. Therefore it is binomial.

(ii) Since 1000 contains one terms. Therefore it is monomial.

(iii) Since Algebraic Expressions and Identities/image049.pngcontains four terms. Therefore it is a polynomial and it does not fit in above three categories.

(iv) SinceAlgebraic Expressions and Identities/image051.png contains three terms. Therefore it is trinomial.

(v) Since Algebraic Expressions and Identities/image052.png contains two terms. Therefore it is binomial.

(vi) SinceAlgebraic Expressions and Identities/image053.png contains three terms. Therefore it is trinomial.

(vii) Since Algebraic Expressions and Identities/image054.pngcontains three terms. Therefore it is trinomial.

(viii) Since Algebraic Expressions and Identities/image055.pngcontains two terms. Therefore it is binomial.

(ix) Since Algebraic Expressions and Identities/image056.pngcontains four terms. Therefore it is a polynomial and it does not fit in above three categories.

(x) Since pqr contains one terms. Therefore it is monomial.

(xi) Since Algebraic Expressions and Identities/image058.pngcontains two terms. Therefore it is binomial.

(xii) Since  2p + 2q contains two terms. Therefore it is binomial.

Question 3.

Add the following:

(i) Algebraic Expressions and Identities/image059.png

(ii) Algebraic Expressions and Identities/image060.png

(iii) Algebraic Expressions and Identities/image061.png

(iv)  Algebraic Expressions and Identities/image062.png

Solution :

 (i)Algebraic Expressions and Identities/image059.png

Algebraic Expressions and Identities/image063.png

Algebraic Expressions and Identities/image064.png

Hence the sum if 0.

Hence the sum is  ab + ac + bc.

Algebraic Expressions and Identities/image067.png

Question 4.

Algebraic Expressions and Identities/image073.png

Solution :

Algebraic Expressions and Identities/image079.png

NCERT Solutions for Class 8 Maths Exercise 9.2

Question 1.

Find the product of the following pairs of monomials:

(i)     Algebraic Expressions and Identities/image001.png

(ii)  Algebraic Expressions and Identities/image003.png   

(iii) Algebraic Expressions and Identities/image003.png

(iv) Algebraic Expressions and Identities/image004.png   

(iv) 4p ,0

Solution :

(i)   Algebraic Expressions and Identities/image006.png = Algebraic Expressions and Identities/image007.png = Algebraic Expressions and Identities/image008.png

(ii)Algebraic Expressions and Identities/image003.png = Algebraic Expressions and Identities/image010.png

= Algebraic Expressions and Identities/image011.png

(iii) Algebraic Expressions and Identities/image012.png= Algebraic Expressions and Identities/image013.png

= Algebraic Expressions and Identities/image014.png

(iv)Algebraic Expressions and Identities/image015.png =Algebraic Expressions and Identities/image016.png

= Algebraic Expressions and Identities/image017.png

(v)Algebraic Expressions and Identities/image018.png= Algebraic Expressions and Identities/image019.png = 0

Question 2.

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

Algebraic Expressions and Identities/image020.png

Solution :

 (i)   Area of rectangle

= Algebraic Expressions and Identities/image021.png

= Algebraic Expressions and Identities/image022.png sq. units

(ii) Area of rectangle

= Algebraic Expressions and Identities/image021.png

= Algebraic Expressions and Identities/image023.png

= 50mn sq. units

(iii) Area of rectangle  = Algebraic Expressions and Identities/image021.png

= Algebraic Expressions and Identities/image025.png

= Algebraic Expressions and Identities/image022.pngsq. units

(iv) Area of rectangle  = Algebraic Expressions and Identities/image021.png

= Algebraic Expressions and Identities/image027.png

= Algebraic Expressions and Identities/image028.png sq. units

(v) Area of rectangle  = Algebraic Expressions and Identities/image021.png

= Algebraic Expressions and Identities/image029.png

= Algebraic Expressions and Identities/image024.png sq. units

Question 3.

Complete the table of products:

(i)
Algebraic Expressions and Identities/image094.PNG    

Solution :

(i)
Algebraic Expressions and Identities/image095.PNG    

Question 4.

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

(i)    Algebraic Expressions and Identities/image061.png    

(ii) Algebraic Expressions and Identities/image062.png

(iii) Algebraic Expressions and Identities/image063.png    

(iv) Algebraic Expressions and Identities/image064.png

Solution :

(i) Volume of rectangular box

Algebraic Expressions and Identities/image065.png

= Algebraic Expressions and Identities/image066.png

= Algebraic Expressions and Identities/image067.pngcubic units

(ii) Volume of rectangular box

Algebraic Expressions and Identities/image065.png

= Algebraic Expressions and Identities/image068.png

= Algebraic Expressions and Identities/image069.png cubic units

(iii) Volume of rectangular box

Algebraic Expressions and Identities/image065.png

= Algebraic Expressions and Identities/image068.png

Algebraic Expressions and Identities/image071.png

= Algebraic Expressions and Identities/image072.png cubic units

(iv) Volume of rectangular box

=Algebraic Expressions and Identities/image065.png

= Algebraic Expressions and Identities/image074.png cubic units

Question 5.

Obtain the product of:

(i)    Algebraic Expressions and Identities/image075.png

(ii) Algebraic Expressions and Identities/image076.png

(iii) Algebraic Expressions and Identities/image077.png   

(iv) Algebraic Expressions and Identities/image078.png

(v) Algebraic Expressions and Identities/image079.png

Solution :

(i)   Algebraic Expressions and Identities/image080.png

= Algebraic Expressions and Identities/image081.png

(ii) Algebraic Expressions and Identities/image082.png= Algebraic Expressions and Identities/image083.png

= Algebraic Expressions and Identities/image084.png

(iii) Algebraic Expressions and Identities/image085.png
Algebraic Expressions and Identities/image086.png

= Algebraic Expressions and Identities/image087.png

(iv)Algebraic Expressions and Identities/image088.png

Algebraic Expressions and Identities/image089.png

=Algebraic Expressions and Identities/image090.png

(v) Algebraic Expressions and Identities/image091.pngAlgebraic Expressions and Identities/image092.png

= Algebraic Expressions and Identities/image093.png

NCERT Solutions for Class 8 Maths Exercise 9.3

Question 1.

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

(i)  Algebraic Expressions and Identities/image001.png

(ii) Algebraic Expressions and Identities/image003.png

(iii) Algebraic Expressions and Identities/image004.png

(iv) Algebraic Expressions and Identities/image004.png

(v)  Algebraic Expressions and Identities/image005.png

Solution :

(i)Algebraic Expressions and Identities/image006.png

= Algebraic Expressions and Identities/image007.png

(ii)Algebraic Expressions and Identities/image008.png

= Algebraic Expressions and Identities/image009.png

(iii)Algebraic Expressions and Identities/image010.png

= Algebraic Expressions and Identities/image011.png

(iv)Algebraic Expressions and Identities/image012.png

= Algebraic Expressions and Identities/image013.png

 (v)Algebraic Expressions and Identities/image014.png = Algebraic Expressions and Identities/image015.png

= 0 + 0 + 0 = 0

Question 2.

Complete the table:

Algebraic Expressions and Identities/image013.png

Solution :

Algebraic Expressions and Identities/image013.png

Algebraic Expressions and Identities/image013.png

Question 3.

Find the product:

(i)  Algebraic Expressions and Identities/image041.png

(ii) Algebraic Expressions and Identities/image042.png

(iii) Algebraic Expressions and Identities/image043.png

(iv) Algebraic Expressions and Identities/image044.png

Solution :

 (i)Algebraic Expressions and Identities/image045.png

Algebraic Expressions and Identities/image046.png

= Algebraic Expressions and Identities/image047.png

(ii) Algebraic Expressions and Identities/image042.png

= Algebraic Expressions and Identities/image048.png

= Algebraic Expressions and Identities/image049.png

(iii)Algebraic Expressions and Identities/image050.png

= Algebraic Expressions and Identities/image051.png

= Algebraic Expressions and Identities/image052.png

(iv) Algebraic Expressions and Identities/image053.png =Algebraic Expressions and Identities/image054.png

Question 4.

(a) Simplify: Algebraic Expressions and Identities/image055.pngand find values for

(i) Algebraic Expressions and Identities/image056.png

(ii) Algebraic Expressions and Identities/image057.png

(b) Simplify: Algebraic Expressions and Identities/image058.png find its value for

(i) Algebraic Expressions and Identities/image059.png

(ii) Algebraic Expressions and Identities/image060.png

(iii) Algebraic Expressions and Identities/image061.png

Solution :

(a) Algebraic Expressions and Identities/image055.png

Algebraic Expressions and Identities/image062.png

= Algebraic Expressions and Identities/image063.png

(i) For Algebraic Expressions and Identities/image064.pngAlgebraic Expressions and Identities/image065.png

= Algebraic Expressions and Identities/image066.png

Algebraic Expressions and Identities/image067.png= 108 – 45 + 3 = 66

(ii) For Algebraic Expressions and Identities/image068.pngAlgebraic Expressions and Identities/image063.png

= Algebraic Expressions and Identities/image069.png

= Algebraic Expressions and Identities/image070.png

= Algebraic Expressions and Identities/image071.png

(b)Algebraic Expressions and Identities/image058.png

Algebraic Expressions and Identities/image072.png

= Algebraic Expressions and Identities/image073.png

(i)  For  a= 0, Algebraic Expressions and Identities/image073.png

= Algebraic Expressions and Identities/image075.png

= 0 + 0 + 0 + 5 = 5

(ii) For a = 1 Algebraic Expressions and Identities/image073.png

= Algebraic Expressions and Identities/image077.png

= 1 + 1 + 1 + 5 = 8

(iii) For Algebraic Expressions and Identities/image078.pngAlgebraic Expressions and Identities/image073.png

= Algebraic Expressions and Identities/image079.png

Algebraic Expressions and Identities/image080.png=Algebraic Expressions and Identities/image081.png =4

Question 5.

(a) Add: Algebraic Expressions and Identities/image082.png and Algebraic Expressions and Identities/image083.png

(b) Add:Algebraic Expressions and Identities/image084.pngand Algebraic Expressions and Identities/image085.png

(c) Subtract: Algebraic Expressions and Identities/image086.png from Algebraic Expressions and Identities/image087.png

(d) Subtract: Algebraic Expressions and Identities/image088.pngfrom Algebraic Expressions and Identities/image089.png

Solution :

(a)Algebraic Expressions and Identities/image090.png

= Algebraic Expressions and Identities/image091.png

= Algebraic Expressions and Identities/image092.png

(b)Algebraic Expressions and Identities/image093.png +

= Algebraic Expressions and Identities/image094.png

= Algebraic Expressions and Identities/image095.png

= Algebraic Expressions and Identities/image096.png

(c)Algebraic Expressions and Identities/image097.png

= Algebraic Expressions and Identities/image098.png

= Algebraic Expressions and Identities/image099.png

= Algebraic Expressions and Identities/image100.png

(d)Algebraic Expressions and Identities/image101.png

= Algebraic Expressions and Identities/image102.png

= Algebraic Expressions and Identities/image103.png

= Algebraic Expressions and Identities/image104.png

= Algebraic Expressions and Identities/image105.png

= Algebraic Expressions and Identities/image106.png

= Algebraic Expressions and Identities/image107.png

NCERT Solutions for Class 8 Maths Exercise 9.4

Question 1.

Multiply the binomials:

(i) Algebraic Expressions and Identities/image001.png and Algebraic Expressions and Identities/image002.png

(ii) Algebraic Expressions and Identities/image003.png and Algebraic Expressions and Identities/image006.png

(iii) Algebraic Expressions and Identities/image005.png and Algebraic Expressions and Identities/image006.png

(iv) image007.pngand image008.png

(v) Algebraic Expressions and Identities/image009.png and Algebraic Expressions and Identities/image010.png

(vi) Algebraic Expressions and Identities/image011.png and Algebraic Expressions and Identities/image012.png

Solution :

(i) Algebraic Expressions and Identities/image013.png

Algebraic Expressions and Identities/image014.png

= Algebraic Expressions and Identities/image015.png

= Algebraic Expressions and Identities/image016.png

= Algebraic Expressions and Identities/image017.png

(ii)Algebraic Expressions and Identities/image018.png

= Algebraic Expressions and Identities/image019.png

= Algebraic Expressions and Identities/image020.png

= Algebraic Expressions and Identities/image021.png

(iii)Algebraic Expressions and Identities/image022.png

Algebraic Expressions and Identities/image023.png

= Algebraic Expressions and Identities/image024.png

= Algebraic Expressions and Identities/image025.png

= Algebraic Expressions and Identities/image026.png

(iv) Algebraic Expressions and Identities/image027.png

= Algebraic Expressions and Identities/image028.png

= Algebraic Expressions and Identities/image029.png

(v)Algebraic Expressions and Identities/image030.png

= Algebraic Expressions and Identities/image031.png

= Algebraic Expressions and Identities/image031.png

= Algebraic Expressions and Identities/image033.png

= Algebraic Expressions and Identities/image034.png

(vi) Algebraic Expressions and Identities/image035.png

Algebraic Expressions and Identities/image036.png

Algebraic Expressions and Identities/image037.png

= Algebraic Expressions and Identities/image038.png

= Algebraic Expressions and Identities/image039.png

= Algebraic Expressions and Identities/image040.png

Question 2.

Find the product:

(i)  Algebraic Expressions and Identities/image041.png

(ii) Algebraic Expressions and Identities/image042.png

(iii) Algebraic Expressions and Identities/image043.png

(iv)  Algebraic Expressions and Identities/image044.png

Solution :

(i)Algebraic Expressions and Identities/image041.png

Algebraic Expressions and Identities/image045.png

= Algebraic Expressions and Identities/image046.png

= Algebraic Expressions and Identities/image047.png= 15 - x -2x²

(ii)Algebraic Expressions and Identities/image042.png

Algebraic Expressions and Identities/image049.png

= Algebraic Expressions and Identities/image050.png

= Algebraic Expressions and Identities/image052.png

(iii) Algebraic Expressions and Identities/image043.png

Algebraic Expressions and Identities/image053.png

= Algebraic Expressions and Identities/image054.png

= Algebraic Expressions and Identities/image055.png

(iv) Algebraic Expressions and Identities/image044.png

Algebraic Expressions and Identities/image056.png

= Algebraic Expressions and Identities/image057.png

= Algebraic Expressions and Identities/image058.png

Question 3.

Simplify:

(i) Algebraic Expressions and Identities/image059.png

(ii) Algebraic Expressions and Identities/image060.png

(iii) Algebraic Expressions and Identities/image061.png

(iv) Algebraic Expressions and Identities/image062.png

(v) Algebraic Expressions and Identities/image063.png

(vi) Algebraic Expressions and Identities/image064.png

(vii) Algebraic Expressions and Identities/image065.png

(viii) Algebraic Expressions and Identities/image066.png

Solution :

(i) Algebraic Expressions and Identities/image067.png

Algebraic Expressions and Identities/image068.png

= Algebraic Expressions and Identities/image069.png

= Algebraic Expressions and Identities/image070.png

= Algebraic Expressions and Identities/image071.png

(ii)Algebraic Expressions and Identities/image072.png

Algebraic Expressions and Identities/image073.png

= Algebraic Expressions and Identities/image074.png

= Algebraic Expressions and Identities/image075.png

= Algebraic Expressions and Identities/image076.png

(iii)Algebraic Expressions and Identities/image077.png

= Algebraic Expressions and Identities/image078.png

= Algebraic Expressions and Identities/image079.png

(iv)Algebraic Expressions and Identities/image080.png

Algebraic Expressions and Identities/image081.png

= Algebraic Expressions and Identities/image082.png

= Algebraic Expressions and Identities/image083.png

= Algebraic Expressions and Identities/image084.png

= 4ac

(v) Algebraic Expressions and Identities/image086.png

Algebraic Expressions and Identities/image087.png

= Algebraic Expressions and Identities/image088.png

= Algebraic Expressions and Identities/image089.png

= Algebraic Expressions and Identities/image090.png

(vi)Algebraic Expressions and Identities/image091.png

Algebraic Expressions and Identities/image092.png

= Algebraic Expressions and Identities/image093.png

= Algebraic Expressions and Identities/image095.png

(vii)Algebraic Expressions and Identities/image096.png

Algebraic Expressions and Identities/image097.png

= Algebraic Expressions and Identities/image098.png

= Algebraic Expressions and Identities/image094.png

= Algebraic Expressions and Identities/image100.png

(viii)Algebraic Expressions and Identities/image096.png

Algebraic Expressions and Identities/image102.png

= Algebraic Expressions and Identities/image103.png

= Algebraic Expressions and Identities/image104.png

= Algebraic Expressions and Identities/image105.png

Notes,worksheet and solved question for Maths class 8

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