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

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                     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

             4x²-2xy+3y²

             7x²-4xy+10y²

•       +      –

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5x²-22y²

Q.5 Subtract the following expression

6x²+4xy+y² ,3x²-xy+3y²

Ans: 

       6x²+4xy+y²

       3x²-xy+3y²

–

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  3x² + 3xy – 2y²    

      

Q.6 Simpify the following

x²(y²–z²) + y²(z²–x²) + z²(x²–y²)

 

Ans: 

        =    x²(y²–z²) + y²(z²–x²) + z²(x²–y²)

         

        =   x² y²– x²z² + y²z² – y²x² + z²x² – z²y² 

       

         =   x² y² – y²x² + y²z² – z²y² – x²z² + 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

Ans:

        =   216x³-64y³

       

=  a³–b³ = (a-b)(a²+b²+2ab)

 =  (6-4)(6²+4²+2*6*4) 

   = 2(36+16+48)

 

    =180   

 

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

 

       xy+yz+zx=40

 

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.1 

 

Q.2

 

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

FAQ

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.