**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 hand in hand to determine a specific situation, Algebra comes into play. As students find these algebra formulas and expressions in Maths may get a little tough to handle, this is where Embibe comes to your rescue.

In this article, we will provide you with a detailed list of Algebraic Expressions in Maths, their definition, and examples. This article will be helpful for all the students who want to get better in Mathematics. You can refer to these algebra formulas provided here while solving the questions.

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## Algebra Formulas: List Of Algebraic Expressions In Maths

Algebra is represented as the study of unknown quantities. Its concepts become important for students studying from Class 6 to the higher classes. This article on Algebra Formulas and Expression covers the following topics.

- Algebraic Identities
- Laws of Exponent
- Quadratic Equations
- List of Important Formulas

*We will cover these aforementioned topics one by one.*

### 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 the 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 coursebook has a lot of questions based on it. So, you need to stay focussed 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 × … 9 more 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 Formulas: 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^{m-n} - a
^{m}x b^{m }= (ab)^{m} - a
^{m}/ b^{m }= (a/b)^{m} - (a/b)
^{-m}=(b/a)^{m} - (1)
= 1 for infinite values of^{n}*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 the equation ax^{2} + bx + c = 0 (where a ≠ 0) can be given as:

\(\frac{-b\:\pm \sqrt{b^2-4ac}}{2a}\)

Some important points about the equation as a part of important algebra formulas are given below:

- Δ = b
^{2}− 4ac is also known as a discriminant. - For roots;
- Δ > 0 happens when the roots are real and distinct
- For real and coincident roots, Δ = 0
- Δ < 0 happens in the case when the roots are non-real

- 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.

### Generic Algebra Formulas

The general algebra formulas can be given as:

**n is a natural number:**a^{n}– b^{n}= (a – b)(a^{n-1}+ a^{n-2}b+…+ b^{n-2}a + b^{n-1})**If n is even:**(n = 2k), a^{n}+ b^{n}= (a – b)(a^{n-1}+ a^{n-2}b +…+ b^{n-2}a + b^{n-1})**n is odd:**(n = 2k + 1), a^{n}+ b^{n}= (a + b)(a^{n-1}– a^{n-2}b +a^{n-3}b^{2}…- b^{n-2}a + b^{n-1})**General square Formula:**(a + b + c + …)^{2}= a^{2}+ b^{2}+ c^{2}+ … + 2(ab + ac + bc + ….)

### 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}]

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### 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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### Take Advantage Of Study Materials On Embibe!

Now you have the list of all the Algebra Formulas in one place. We hope this article will help you in your preparation. In addition to this, Embibe has prepared a lot of academic articles pertaining to these formulas on a number of topics. You can refer to them anytime and achieve great scores. Make sure to check out more of such formulas in the below links.

Maths Formulas For Class 11 | Maths Formulas For Class 12 |

Algebraic Expressions | Trigonometric Ratios |

Maths Formulas For Class 8 | Mensuration Formulas |

Trigonometry Formulas | Trigonometry Table |

*If you have any questions regarding this article on Algebraic formulas and expressions, you can drop your queries down in the comment sections below. We will surely help you out at the earliest.*

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