Algebra Formulas: Mathematics typically covers a vast area and is one of the important fields of study. As students approach higher classes, they get introduced to Algebra. When the fixed and dynamic components come handinhand to determine a specific situation, Algebra comes into play. If you find algebra formulas and expressions a little tough to handle, we at Embibe have come to your rescue.
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In this article, we will provide you with a detailed list of Algebraic Expressions and formulas in Maths, their definitions, and examples. This article will be helpful for all students who want to score more marks in Mathematics. You can also refer to the algebra formulas PDF provided here while solving the questions.
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Algebra Formulas: List Of Algebraic Expressions In Maths  Algebra Formula List
Algebra is the study of unknown quantities. Its concepts become important for students studying from Class 6 to the higher classes. This article on important algebra formulas and expressions covers the following topics.
 Algebraic Identities
 Laws of Exponent
 Quadratic Equations
 List of Important Formulas
We will cover these aforementioned topics one by one.
Other important Maths formulas:
Algebra Formulas: Important Algebraic Identities
Algebraic identities comprise various equality equations consisting of different variables.
 a) Linear Equations in One Variable: A linear equation in one variable has the maximum of one variable present in order 1. It is depicted in the form of ax + b = 0, where x is represented as the variable.
 b) Linear Equations in Two Variables: A linear equation in two variables consists of the utmost two variables present in order 2. The equation is depicted in the form: ax^{2} + bx + c = 0. The two variables are quite important because your course book has a lot of questions based on it. So, you need to stay focused on important algebra formulas to find the solution.
Some basic identities to note are:
 The combination of literal numbers obeys every basic rule of addition, subtraction, multiplication and division.
 x × y = xy; such as 5 × a = 5a = a × 5.
 a × a × a × … 12 times = a^{12}
 If a number is x^{8}, then x is the base and 8 is the exponent.
 A constant is a symbol with a fixed numerical value.
Algebra Formula: Laws Of Exponent
Exponents are the powers or the degrees in any mathematical expression. Here are some laws of exponents important in learning algebra formulas (given below):
 a^{0} = 1
 a^{m} = 1/a^{m}
 (a^{m})^{n} = a^{mn}
 a^{m} / a^{n} = a^{mn}
 a^{m} x b^{m }= (ab)^{m}
 a^{m} / b^{m }= (a/b)^{m}
 (a/b)^{m} = (b/a)^{m}
 (1)^{n} = 1 for infinite values of n.
Algebra Formulas: Quadratic Equations
Quadratic equations are simply the linear equations in two variables. These are quite important when it comes to solving mathematical questions.
The roots of a quadratic equation ax^{2} + bx + c = 0 (where a ≠ 0) can be given as:
\(\frac{b\:\pm \sqrt{b^24ac}}{2a}\)
Some important points about the equation as a part of important algebra formulas are given below:
 D = b^{2} − 4ac is also known as the discriminant of quadratic equation.
 For roots;
 (i) D> 0 happens when the roots are real and distinct
 (ii) For real and coincident roots, D = 0
 (iii) D< 0 happens in the case when the roots are nonreal
 If α and β are the two roots of the equation ax^{2} + bx + c then,
α + β = (b / a) and α × β = (c / a).  If the roots of a quadratic equation are α and β, the equation will be
(x − α)(x − β) = 0.
Important Algebra Formulas
The general algebra formulas can be given as:
 n is a natural number: a^{n} – b^{n} = (a – b)(a^{n1} + a^{n2}b+…+ b^{n2}a + b^{n1})
 If n is even: (n = 2k), a^{n} + b^{n} = (a – b)(a^{n1} + a^{n2}b +…+ b^{n2}a + b^{n1})
 n is odd: (n = 2k + 1), a^{n} + b^{n} = (a + b)(a^{n1} – a^{n2}b +a^{n3}b^{2}… b^{n2}a + b^{n1})
 General square Formula: (a + b + c + …)^{2} = a^{2} + b^{2} + c^{2} + … + 2(ab + ac + bc + ….)
Algebraic Expressions Formulas: List Of Important Algebra Formulas
Here is a complete list of all the important algebra formulas:
 (a + b)^{2} = a^{2} + 2ab + b^{2}
 (a – b)^{2} = a^{2} – 2ab + b^{2}
 (a + b) (a – b) = a^{2} – b^{2}
 (x + a) (x + b) = x^{2} + (a + b) x + ab
 (x + a) (x – b) = x^{2} + (a – b) x – ab
 (x – a) (x + b) = x^{2} + (b – a) x – ab
 (x – a) (x – b) = x^{2} – (a + b) x + ab
 (a + b)^{3} = a^{3} + b^{3} + 3ab (a + b)
 (a – b)^{3} = a^{3} – b^{3} – 3ab (a – b)
 (a + b)^{4} = a^{4} + 4a^{3}b + 6a^{2}b^{2} + 4ab^{3} + b^{4}
 (a – b)^{4} = a^{4} – 4a^{3}b + 6a^{2}b^{2} – 4ab^{3} + b^{4}
 (x + y + z)^{2} = x^{2} + y^{2} + z^{2} + 2xy +2yz + 2xz
 (x + y – z)^{2} = x^{2} + y^{2} + z^{2} + 2xy – 2yz – 2xz
 (x – y + z)^{2} = x^{2} + y^{2} + z^{2} – 2xy – 2yz + 2xz
 (x – y – z)^{2} = x^{2} + y^{2} + z^{2} – 2xy + 2yz – 2xz
 x^{3} + y^{3} + z^{3} – 3xyz = (x + y + z) (x^{2} + y^{2} + z^{2} – xy – yz xz)
 x^{2 }+ y^{2} = \(\frac{1}{2}\) [(x + y)^{2} + (x – y)^{2}]
 (x + a) (x + b) (x + c) = x^{3 }+ (a + b + c)x^{2} + (ab + bc + ca)x + abc
 x^{3} + y^{3} = (x + y) (x^{2 }– xy + y^{2})
 x^{3} – y^{3} = (x – y) (x^{2 }+ xy + y^{2})
 x^{2} + y^{2} + z^{2} – xy – yz – zx = \(\frac{1}{2}\) [(x – y)^{2} + (y – z)^{2} + (z – x)^{2}]
Download Maths formulas for Class 6 to 12:
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Maths Formulas for Class 8  Maths Formulas for Class 9 
Maths Formulas for Class 10  Maths Formulas for Class 11 
Maths Formulas for Class 12  — 
Algebraic Formula List: Frequently Asked Questions (FAQs) Related To Algebra Formulas
Let’s look at some of the important FAQs related to Algebra formulas below:
Q1: Why Algebra is considered important in Mathematics?
Ans: Algebra is an important concept in applied mathematics. It is undeniably the best component that can help you understand the theory of partial differential equations. These are quite important in physical systems such as movement and forces as well as heat transfers, and more. Therefore, to stay clear of these physical aspects, you need to be proficient with the basics of algebra formulas and equations.
Q2: Where can I practice Algebra questions?
Ans: You can practice Algebra questions at Embibe. Embibe provides unlimited algebra practice questions and algebra mock questions created by academic experts. You can even post your questions at Embibe’s Ask platform and get their solutions.
Q3: What are the different components of the Algebra formulas and expressions?
Ans: Algebra formulas and expressions can be divided into the following components:
1. Algebraic Identities
2. Laws of Exponent
3. Quadratic Equations
4. Other Important Expressions
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Now you have the list of all the Algebra formulas in one place. These formulas will help all students from Class 6 to 12. We hope this article helps you in your preparation. In addition to this, Embibe offers free Mock Tests and Practice Questions for Class 8 to 12. You can refer to them anytime and achieve great scores.
Solve Algebra Practice Questions on Embibe for free and go through the hints and solutions whenever required. Your problemsolving speed and accuracy will improve remarkably.
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