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. 9x^{3}yz
Q.2 What is the coefficient of

9x^{3}yz

4x^{2}y3z

6yz3y

4yz5x

67x^{3}54y
Ans: 1. 9
2. 4,3
3. 6.3
4. 4,5
5. 67,54
Q.3 Add the following expressions
5a^{2}b^{2}, 4a^{2}b^{2}, 2/3 a^{2}b^{2}
Ans: 5a^{2}b^{2}+ 4a^{2}b^{2}+ 2/3 a^{2}b^{2}
= –a^{2}b^{2} + 2/3 a^{2}b^{2}
= 3a^{2}b^{2} + 2a^{2}b^{2}/3
= –a^{2}b^{2}/3.
Q.4 Add the following expressions
8x^{2}+6xy+9y^{2} ,4x^{2}2xy+3y^{2}, 7x^{2}4xy+10y^{2}
Ans: 8x^{2}+6xy+9y^{2}
4x^{2}2xy+3y^{2}
7x^{2}4xy+10y^{2}

+ –
5x^{2}22y^{2}
Q.5 Subtract the following expression
6x^{2}+4xy+y^{2} ,3x^{2}xy+3y^{2}
Ans:
6x^{2}+4xy+y^{2}
3x^{2}xy+3y^{2}
–
3x^{2} + 3xy – 2y^{2 }
Q.6 Simpify the following
x^{2}(y^{2}–z^{2}) + y^{2}(z^{2}–x^{2}) + z^{2}(x^{2}–y^{2})
Ans:
= x^{2}(y^{2}–z^{2}) + y^{2}(z^{2}–x^{2}) + z^{2}(x^{2}–y^{2})
= x^{2} y^{2}– x^{2}z^{2} + y^{2}z^{2} – y^{2}x^{2} + z^{2}x^{2} – z^{2}y^{2}
= x^{2} y^{2} – y^{2}x^{2} + y^{2}z^{2} – z^{2}y^{2} – x^{2}z^{2} + z^{2}x^{2}
= 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
216x^{3}64y^{3}
Ans:
= 216x^{3}64y^{3}
= a^{3}–b^{3} = (ab)(a^{2}+b^{2}+2ab)
= (64)(6^{2}+4^{2}+2*6*4)
= 2(36+16+48)
=180
Q.2 Factorize x^{2}+yxyx
Ans: x^{2}+yxyx
= x^{2}x+yxy
= x(x1)y(x1)
= (xy)(x1)
Q.3 Factorize x(x2)(x4)+4x8
Ans: x(x2)(x4)+4x8
= x(x2)(x4)+4(x2)
= (x2)[x(x4)+4]
= (x2)[x^{2}4x+4]
= (x2)(x2)^{2 }
= (x2)^{3} .
Q.4 Solve 32x^{3}+108y^{3}
Ans: 32x^{3}+108y^{3}
Take 4 common.
=4(8x^{3} + 27y^{3})
According to formula a^{3}+b^{3} = (a+b)(a^{2}+b^{2}2ab)
= 4[(2+3)(2^{2}+3^{2}+2*2*3)]
= 4[5(4+9+12)]
= 500.
Q.5 If x+y+z= 9 and xy+yz+zx=40 then find x^{2}+y^{2}+ z^{2}
Ans: Given
x+y+z= 9
xy+yz+zx=40
According to formula
9^{2} = x^{2}+y^{2}+ z^{2}+2(40)
81 = x^{2}+y^{2}+ z^{2}+80
x^{2}+y^{2}+ z^{2} = 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.
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