Algebra Formulas - Basic Algebraic Formulas and Expression
Starting from computer science to engineering, the importance of algebra is manifold in nearly every career choice. So, learners must grasp every algebra formula to prepare themselves for calculations beyond basic math. Not only for learners in school but even candidates appearing for competitive exams should have a firm grasp of algebraic formulae to excel.
“Algebra can be your stepping stone of success, opening doors of opportunities and excellent discoveries.”
Vedantu brings a comprehensive algebra formulas list to aid students in learning its basic as well as advanced concepts effortlessly.
Do You Know?
Algebra was introduced by the Greeks back in the 3rd century.
It was the Babylonians who created the algebraic equation and formulae we still use in the 21st century to solve diverse problems.
Modern algebra was brought in by Rene Descartes in the 16th century.
Sounds a Bit Exciting?
Here’s what is involved in the study of algebra.
The study of algebra revolves around in-depth learning of terms, concepts and formulae. The idea is simple. Here, mathematical symbols, known as variables, represent quantity without having any fixed value and these are manipulated to derive solutions.
Basic Example:
Algebra asks questions like what is the value of x if x + 7 = 10? To get the result, you need to do another calculation, i.e. 10 – 7 = 3. So, the value of x is 3.
Once you learn the basics (elementary algebra), advanced levels gradually become easier.
Master algebra for its many perks!
Well, we understand how tedious studying these alphanumerical formulae can be. However, if you know the perks of mathematics formula algebra in real life, you may find it convincing enough to learn. Here you go!
As algebraic formulae are rules that work in every circumstance, these largely help in decision making.
Studying it enables you to think logically and resolve complex problems efficiently.
Many subjects such as engineering, physics, chemistry, etc. need algebra. So, mastering the concepts and formulae can significantly help you in higher studies.
Without algebra, the internet, Google, digital televisions, mobile phones and other advanced technology would not have existed. It signifies that learning maths algebra formula can prepare you for a career in the technology sector.
Above all, mathematics teachers and toppers also recommend studying the formulae as these can save a lot of time during the examination.
What to Expect From Vedantu?
Whether you are in Class 6 or Class 12, Vedantu has a list of all algebra formulas essential in every syllabus.
Students can access the formulae anytime they want free of cost.
Learners of CBSE Board from Class 6 to Class 12 can also download chapter-wise math formulae in PDF format.
Vedantu adopts a unique way of solving various math problems with equations. It helps students understand their use rather than merely memorizing formulae.
Students can access important revision notes and questions to practise and learn.
Besides these, you can access essential study materials from Vedantu like RS Aggarwal Solutions, RD Sharma solutions, NCERT solutions, etc. These can further enhance the concepts of algebra and the application of every formula.
In all, Vedantu endeavors to support students in learning the most complex lessons of mathematics in the simplest way possible.
Various Algebraic Formulas & Expression
a2−b2=(a+b)(a−b)
(a+b)2=a2+2ab+b2
a2+b2=(a−b)2+2ab
(a−b)2=a2−2ab+b2
(a+b+c)2=a2+b2+c2+2ab+2ac+2bc
(a−b−c)2=a2+b2+c2−2ab−2ac+2bc
(a+b)3=a3+3a2b+3ab2+b3;(a+b)3=a3+b3+3ab(a+b)
(a−b)3=a3−3a2b+3ab2−b3
a3−b3=(a−b)(a2+ab+b2)
a3+b3=(a+b)(a2−ab+b2)
(a+b)4=a4+4a3b+6a2b2+4ab3+b4
(a−b)4=a4−4a3b+6a2b2−4ab3+b4
a4−b4=(a−b)(a+b)(a2+b2)
a5−b5=(a−b)(a4+a3b+a2b2+ab3+b4)
(x+y+z)2=x2+y2+z2+2xy+2yz+2xz
(x+y−z)2=x2+y2+z2+2xy−2yz−2xz
(x−y+z)2=x2+y2+z2−2xy−2yz+2xz
(x−y−z)2=x2+y2+z2−2xy+2yz−2xz
x3+y3+z3−3xyz=(x+y+z)(x2+y2+z2−xy−yz−xz)
x2+y2=1/2[(x+y)2+(x−y)2]
(x+a)(x+b)(x+c)=x3+(a+b+c)x2+(ab+bc+ca)x+abc
x3+y3=(x+y)(x2−xy+y2)
x3−y3=(x−y)(x2+xy+y2)
x2+y2+z2−xy−yz−zx=1/2[(x−y)2+(y−z)2+(z−x)2]
If n is a natural number, an−bn=(a−b)(an−1+an−2b+...+bn−2a+bn−1)
If n is even (n=2k),an+bn=(a+b)(an−1−an−2b+...+bn−2a−bn−1)
If n is odd (n=2k+1),an+bn=(a+b)(an−1−an−2b+...−bn−2a+bn−1)
(a+b+c+...)2=a2+b2+c2+...+2(ab+bc+....)
Laws of Exponents
(am)(an)=am+n
(ab)m=ambm
(am)n=amn
Fractional Exponents
a0=1
am/an=am−n
am=1/a−m
a−m=1/am
Practice Problem:
Find value of (3 + 7)2
Solution: Using formula (a+b)2=a2+b2+2ab
(3+7)2=32+72+2(3)(7) =9+49+42
=100
Find the value of (4 + 3 − 2)2
Solution: Using formula (a+b+c)2=a2+b2+c2+2ab+2ac+2bc
= (4+3+(-2))2=42+32+(-2)2+2*4*3 +2*4*(-2)+2*3*(-2)
= 25
Few Algebraic Properties
Addition's commutative property: a + b = b + a
If the order of the elements is modified, the sum of the expression does not change. Expressions or numbers can be used as elements.
Multiplication's Commutative Property: a x b = b x a
The product does not change when the order of the factors is changed. Numbers or phrases can be used as these factors.
Addition's Associative Property: (a + b)+ c = a + (b + c)
The property states that when two or more numbers are brought together to execute basic arithmetic addition, the order of the numbers has no bearing on the outcome.
Multiplication has an associative property: (a x b) xc = a x (b x c)
When two or more factors are joined together in fundamental arithmetical multiplication, the order of the elements has no effect on the final result. Also, in this situation, parenthesis is used to organize the items.
Addition and Multiplication have distributive properties:
a × (b + c) = a × b + a × c and (a + b) × c = a × c + b × c
The distributive property states that multiplying each element by a single term and then adding and subtracting the products is the same as multiplying each element by a single term and then adding and subtracting the products.
Rule of multiplication over subtraction: p (q-r) = p*q – p*r
if p, q, and r are all integers. Similarly, the left and right distributions can be used in the addition rule for multiplication over subtraction.
Left distributive law if p* (q-r) = (p * q) – (p*r)- and
Right distributive law if (p-q)*r = (p*r) – (q*r)-
Algebraic Identities
Algebraic Identities Math expressions that include numbers, variables (unknown values), and mathematical operations are known as algebraic equations (addition, subtraction, multiplication and division).
Algebraic identities are used in many areas of mathematics, including algebra, geometry, and trigonometry. These are primarily used to find the polynomial factors.
Laws of Exponents
To solve the complex exponential expressions, a few of the ordinary laws of exponents are used, with the same base having several powers and other bases having the same power. Students can simply compute greater exponential values without having to expand the exponential terms. These exponential rules can also be used to derive some logarithmic laws.
am⋅an=am+n
am/an=am–n
(am)n=an
(ab)m=am⋅bm
a0=1
a–m=1/am
FAQs on Algebra Formula
1. What is the definition of algebra?
Algebra is a form of arithmetic in which numbers are represented by letters, sometimes known as literal numbers or simply literals.
These letters are referred to as variables because they do not have any set values. We see several values that are constantly changing in our real-life scenarios. However, the necessity to express these changing values is constant.
These values are commonly represented in algebra by letters such as a,b,c,x,y,z,p, or q, and these letters are referred to as variables. In addition, the values of these letters are modified by other arithmetic operations such as addition, subtraction, multiplication, and division. We can create algebraic expressions using these arithmetic operations and letters.
2. What are Algebraic Expressions and How Do I Use Them?
An algebraic expression is a set of constants and variables related by some or all of the four fundamental operations addition (+), subtraction (), multiplication (), and division ().
Example: 4x+5,10y–5 are examples of algebraic expression, and so on.
3. What is the general formula in algebra?
The general algebra formulas that are used are given below:
(a+b)2=a2+2ab+b2
(a–b)2=a2–2ab+b2
(a+b)(a–b)=a2–b2
(x+a)(x+b)=x2+x(a+b)+ab
4. What are Algebraic Identities and how do they work?
An identity is an equation that holds true for all values of the variables in it. The algebraic identities are equations in which the left-hand side of the equation equals the right-hand side of the equation in exactly the same way.
Consider the linear equation ax+b=0 as an example.
When x = -b/a, the left and right sides of the preceding equations are the same.
5. Where can I obtain Algebra Formula notes and questions?
You can find questions on the Algebra Formula on Vedantu. It provides a number of algebraic formulae and identities that students should be familiar with. For students in grades 1 through 12, Vedantu also provides study materials and a variety of competitive exams. The contents include notes, important topics and questions, revision notes, and other things. On Vedantu, you may access all of these resources for free. To use all of these resources, students must first register on the Vedantu website. You can also register through Vedantu's mobile app.