Most Common Questions About Algebra- Class 8 to 10

Most Common Questions About Algebra- Class 8 to 10

Algebra is the representation of mathematical expressions into algebraic forms by using letters and symbols. 

We use different variables like a,b,c or x,y,z, etc., and manipulate them using various math symbols like addition, subtraction, multiplication, and division to obtain desired mathematical expressions.

For example 

 If x + y = 5 and x – y = 7 then what is the value of x?


                     x + y = 5

                     x – y = 7


                     2x = 12

                      x = 6 


Important Algebra’s Formula 

The algebraic formulas are the cornerstone of solving various complex problems. Here we have listed the most important formulas that are often used while solving algebraic equations. Students can get the pdf of the maths formula to learn more. 

Important algebraic formulas


Important Exponential Formulas


Algebraic Questions of Class 8

Q.1 Give the two examples of monomials.

Ans: The two examples of monomials are

          1. 3yx

          2. 9x3yz


Q.2 What is the coefficient of

  1. 9x3yz

  2. 4x2y-3z

  3. 6yz-3y

  4. 4yz-5x

  5. 67x3-54y


Ans: 1. 9

         2. 4,-3

         3. 6.-3

         4. 4,-5

         5. 67,-54


Q.3 Add the following expressions

-5a2b2, 4a2b2, 2/3 a2b2

Ans:    -5a2b2+ 4a2b2+ 2/3 a2b2

         =    –a2b2 + 2/3 a2b2

        =       -3a2b2 + 2a2b2/3

         =            a2b2/3.


Q.4 Add the following expressions

8x2+6xy+9y2 ,4x2-2xy+3y2, 7x2-4xy+10y2 

Ans:     8x2+6xy+9y2



  •       +      –


Q.5 Subtract the following expression

6x2+4xy+y2 ,3x2-xy+3y2





  3x2 + 3xy – 2y2    


Q.6 Simpify the following

x2(y2z2) + y2(z2x2) + z2(x2y2)



        =    x2(y2z2) + y2(z2x2) + z2(x2y2)


        =   x2 y2x2z2 + y2z2y2x2 + z2x2 z2y2 


         =   x2 y2y2x2 + y2z2 z2y2x2z2 + z2x2  


        =     0


Important Algebra’s Questions of Class 9

Here we have provided solved algebraic questions. If you want to practice different types of questions then check out the important questions for class 9 maths.

Q.1 Factorize the the following equation



        =   216x3-64y3


a3b3 = (a-b)(a2+b2+2ab)

 =  (6-4)(62+42+2*6*4) 

   = 2(36+16+48)




Q.2 Factorize x2+y-xy-x


Ans: x2+y-xy-x


     =  x2-x+y-xy


   = x(x-1)-y(x-1)


    = (x-y)(x-1)


Q.3 Factorize x(x-2)(x-4)+4x-8


Ans:     x(x-2)(x-4)+4x-8


           =  x(x-2)(x-4)+4(x-2)


        =  (x-2)[x(x-4)+4]


       =  (x-2)[x2-4x+4]


        = (x-2)(x-2)2   


      =  (x-2)3


Q.4 Solve 32x3+108y3


Ans: 32x3+108y3


Take 4 common.


=4(8x3 + 27y3)


According to formula a3+b3 = (a+b)(a2+b2-2ab)


= 4[(2+3)(22+32+2*2*3)]


= 4[5(4+9+12)]


= 500.


Q.5 If x+y+z= 9 and xy+yz+zx=40 then find x2+y2+ z2


Ans: Given


        x+y+z= 9




According to formula

              92 = x2+y2+ z2+2(40)


              81 = x2+y2+ z2+80

         x2+y2+ z2 = 1.


Algebraic geometry Questions for Class 10

Check out the most important algebraic geometry questions for class 10. 






Q.3 Find the value of x, if the distance between the points(x,-1) and (3,2) is 5.


Q1. What are the different types of algebra?

Ans- Algebra is divided into five subsections named as elementary algebra, abstract algebra, linear algebra, commutative algebra and advanced algebra.

Q2. What is an algebra in mathematical terms?

Ans- It is part of mathematics that helps in the representation of problems and the situations in the form of mathematical equations. In algebra, we use numbers like 4, -5, 0.007 etc and variables like x, y, z etc. 

Q3. What are the three rules of algebra?

Ans- The three rules of algebra are: distributive, commutative and associative algebra which represents different identities of algebra.

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