Algebra is a fundamental branch of mathematics that deals with symbols and the rules for manipulating those symbols to solve equations and understand relationships between quantities. One of the essential algebraic formulas is the expansion of $(a+b_{3}$. This formula, known as the cube of a binomial, is expressed as $(a+b_{3}=a_{3}+3a_{2}b+3ab_{2}+b_{3}$. Understanding and applying this identity is crucial for solving complex algebraic problems efficiently.
For students and professionals who seek a comprehensive understanding of algebraic identities, having a wellorganized list or chart is invaluable. These resources not only provide quick references but also aid in better grasping the concepts by offering visual representations. To cater to this need, we have compiled a detailed PDF encompassing all major algebraic identities. This includes formulas like the square of a binomial, the difference of squares, and the sum and difference of cubes, among others.
Our downloadable PDF chart serves as a handy tool for anyone looking to master algebra. Whether you are a student preparing for exams, a teacher creating lesson plans, or a professional brushing up on your skills, this comprehensive list of algebraic identities will be an indispensable resource in your mathematical toolkit.
Algebra is a branch of mathematics that uses letters to represent numbers. In an algebraic equation, the operations performed on one side of the equation must also be performed on the other side to maintain balance. While mathematical numbers are constants, algebra also encompasses real numbers, complex numbers, matrices, vectors, and more. Commonly used variables in algebraic problems and equations include X, Y, A, and B.
Algebra Formulas
Algebra formulas form the foundation for many critical topics in mathematics. Equations, quadratic equations, polynomials, coordinate geometry, calculus, trigonometry, and probability all rely heavily on algebraic formulas to understand and solve complex problems.
Definition of Algebra Formulas
Algebra formulas are a vital part of Class 10 mathematics in India. Algebra is one of the most crucial areas of mathematics, encompassing numerous topics such as quadratic equations, polynomials, coordinate geometry, calculus, trigonometry, probability, and more. These formulas use a combination of numbers and letters, with common variables being X, Y, A, and B. Algebraic formulas allow us to solve timeconsuming algebraic problems quickly and efficiently. Here, we provide all significant algebraic formulas along with their solutions, making them accessible to students in one place.
Algebra formulas are essentially algebraic equations composed of mathematical phrases and symbols. These formulas typically include an unknown variable $x$, which is revealed during the simplification of an equation. Algebraic formulas are useful for solving complex algebraic computations in a straightforward manner.
For example:
$(a+b_{3}=a_{3}+3a_{2}b+3ab_{2}+b_{3}$
In the formula above, both sides are algebraic expressions. The expression $a_{3}+3a_{2}b+3ab_{2}+b_{3}$ is the simplified form of $(a+b_{3}$.
Algebraic Formulas and Identities
In algebra, an identity is an equation that holds true for all values of the variables involved. An algebraic identity means that the lefthand side (LHS) of the equation is exactly equal to the righthand side (RHS) for any value of the variables. These identities are particularly useful for solving equations and simplifying expressions. Here are some commonly used algebraic identities:
Algebraic Identities Formulas
 $(a+b_{2}=a_{2}+2ab+b_{2}$
 $(a−b_{2}=a_{2}−2ab+b_{2}$
 $(a+b)(a−b)=a_{2}−b_{2}$
 $(x+a)(x+b)=x_{2}+x(a+b)+ab$
Algebra Formulas for Squares (Class 10)
Here are some important formulas involving squares:
 $a_{2}−b_{2}=(a−b)(a+b)$
 $(a+b_{2}=a_{2}+2ab+b_{2}$
 $a_{2}+b_{2}=(a+b_{2}−2ab$
 $(a−b_{2}=a_{2}−2ab+b_{2}$
 $(a+b+c_{2}=a_{2}+b_{2}+c_{2}+2ab+2bc+2ca$
 $(a−b−c_{2}=a_{2}+b_{2}+c_{2}−2ab+2bc−2ca$
These formulas are fundamental in algebra and are essential tools for solving various mathematical problems.
Algebra Formulas for Cube of SSC CGL
Here are some Algebraic formulas involving cubes.
• (a + b)³ = a³+ 3a²b + 3ab²+ b³
• (a + b)³ = a³ + b³ + 3ab(a + b)
• (a – b)³= a³ – 3a²b + 3ab² – b³
• (a – b)³= a³ – b³ – 3ab(a – b)
• a³ – b³ = (a – b)(a²+ ab + b²)
• a³ + b³ = (a + b)(a²– ab + b²)
Some more Algebra formulas are –
• (a + b)⁴= a⁴+ 4a³b + 6a²b² + 4ab³ + b²
• (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)
Algebra Formulas for Natural Numbers
Natural numbers are the positive integers starting from 1 and increasing without bound (i.e., from 1 to infinity). These numbers exclude 0 and negative numbers. Several algebraic formulas are commonly used when performing operations on natural numbers. Let’s consider $n$ to be a natural number.
Key Formulas

Difference of Powers:
$a_{n}−b_{n}=(a−b)(a_{n−}+a_{n−}b+⋯+ab_{n−}+b_{n−})$ 
Sum of Powers (for even $n$):
$a_{n}+b_{n}=(a+b)(a_{n−}−a_{n−}b+⋯+ab_{n−}−b_{n−})wherenis even$ 
Sum of Powers (for odd $n$):
$a_{n}+b_{n}=(a+b)(a_{n−}−a_{n−}b+a_{n−}b_{2}−⋯−b_{n−}a+b_{n−})wherenis odd$
Laws of Exponents
In algebra, an exponent (or power) represents repeated multiplication of a number. For example, $3×3×3×3$ can be written as $_{4}$, where 4 is the exponent of 3. Exponents indicate how many times a number is multiplied by itself. The rules for operating with exponents in addition, subtraction, and multiplication can be easily solved using algebraic formulas.
Basic Rules of Exponents

Product of Powers Rule:
$a_{m}⋅a_{n}=a_{m+n}$ 
Quotient of Powers Rule:
$aa =a_{m−n}(form>n)$ 
Power of a Power Rule:
$(a_{m}_{n}=a_{m⋅n}$ 
Power of a Product Rule:
$(ab_{n}=a_{n}⋅b_{n}$ 
Power of a Quotient Rule:
$(ba )_{n}=ba $
These formulas and rules are fundamental in algebra and are widely used for simplifying and solving equations involving natural numbers.
Algebra Formulas for Quadratic Equations
Algebra formulas for quadratic equations are crucial topics in the Class 9 and 10 syllabus. To find the roots of a given quadratic equation, we use the following formulas:a+b whole cube
If $ax_{2}+bx+c=0$ is a quadratic equation, then:
Based on the given formula, we can conclude the following if the roots of the quadratic equation are α and β:a+b whole cube
 The equation will be $(x−α)(x−β)=0$.
 The sum of the roots $(α+β)$ is equal to $−ab $, and the product of the roots $(α×β)$ is equal to $ac $.
Algebra Formulas List and Sheet
Here is a comprehensive list of all important algebraic formulas. Students should review this list to solve complex algebraic equations quickly and efficiently.
Important Formulas  
1  a²– b² = (a – b)(a + b) 
2  (a + b)²= a²+ 2ab + b² 
3  a²+ b²= (a + b)²– 2ab 
4  (a – b)² = a²– 2ab+ b² 
5  (a + b + c)² = a² + b² + c²+ 2ab + 2bc + 2ca 
6  (a – b – c)² = a²+ b²+ c²– 2ab + 2bc – 2ca 
7  (a + b)³ = a³+ 3a²b + 3ab²+ b³ 
8  (a + b)³ = a³ + b³ + 3ab(a + b) 
9  (a – b)³= a³ – 3a²b + 3ab² – b³ 
10  (a – b)³= a³ – b³ – 3ab(a – b) 
11  a³ – b³ = (a – b)(a²+ ab + b²) 
12  a³ + b³ = (a + b)(a²– ab + b²) 
13  (a + b)⁴= a⁴+ 4a³b + 6a²b² + 4ab³ + b² 
14  (a – b)⁴= a4 – 4a³b + 6a²b² – 4ab³+ b⁴ 
15  a⁴ – b⁴= (a – b)(a + b)(a² + b²) 
16  a⁵ – b⁵= (a – b)(a⁴ + a³b + a²b² + ab³+ b⁴) 
Square of the Sum of Three Terms (a+b+c):
The square of the sum of three terms, a+b+c, expands using the formula for the square of a trinomial:
(a+b+c)2=a2+b2+c2+2ab+2ac+2bc
This formula gives the sum of the squares of each individual term (a^2, b^2, c^2) and twice the product of each pair of terms (2ab, 2ac, 2bc). It applies universally for any values of a, b, and c.
Square of the Difference Between Two Terms (a−b):
The square of the difference between two terms, a−b, expands using the formula for the square of a binomial:
(a−b)2=a2−2ab+b2
Here, the formula provides the square of the first term (a^2), minus twice the product of the two terms (2ab), and the square of the second term (b^2). This expansion holds true for any values of a and b.
Square of the Sum of Two Terms (a+b):
The square of the sum of two terms, a+b, expands using the formula for the square of a binomial:
(a+b)2=a2+2ab+b2
This formula results in the sum of the squares of each individual term (a^2 and b^2) and twice the product of the terms (2ab). It applies universally for any values of a and b.
Example 1: Find the value of $2_{2}−1_{2}$.
Solution: To solve this equation, we use the formula $a_{2}−b_{2}=(a+b)(a−b)$.
$2_{2}−1_{2}=(20+15)(20−15)=35×5=175(Answer)$
Example 2: Given $x−y=2$ and $x_{2}+y_{2}=20$, find the values of $x$ and $y$ (where $x,y>0$).
Solution: From $x_{2}+y_{2}=20$:
$(x−y_{2}+2xy=20_{2}+2xy=204+2xy=202xy=16xy=8$
Now, $(x+y_{2}=(x−y_{2}+4xy=4+32=36$:
$x+y=±6x+y=6(sincex,y>0)(1)x−y=2(2)$
Solving equations (1) and (2):
$x=4,y=2(Answer)$
Example 3: Divide $a_{3}+b_{3}+c_{3}−3abc$ by $a+b+c$ and find the quotient.
Solution:
$a_{3}+b_{3}+c_{3}−3abc=(a+b+c)(a_{2}+b_{2}+c_{2}−ab−ac−bc)Quotient=a+b+c(a+b+c)(a+b+c−ab−ac−bc) =a_{2}+b_{2}+c_{2}−ab−ac−bcMagnitude of quotient is2(Answer)$
Example 4: Find the successive products $(x+y),(x−y),(x_{2}+y_{2})$.
Solution:
$(x+y)(x−y)(x_{2}+y_{2})=(x_{2}−y_{2})(x_{2}+y_{2})=x_{4}−y_{4}(Answer)$
These examples are now rewritten for clarity and correctness.
 Given $x+y=3$ and $xy=2$, find the value of $(x−y_{2}$.
 If $a+b=8$ and $ab=15$, determine the values of $a$ and $b$.
 If $a+b=5$ and $ab=6$, find the value of $a_{2}−b_{2}$.
 For $x=29$ and $y=14$, calculate $4x_{2}+9y_{2}+12xy$.
And here are some algebraic identity formulas in Hindi:
बीजगणित सूत्र:
 $a_{2}−b_{2}=(a−b)(a+b)$
 $(a+b_{2}=a_{2}+2ab+b_{2}$
 $a_{2}+b_{2}=(a+b_{2}−2ab$
 $(a−b_{2}=a_{2}−2ab+b_{2}$
 $(a+b+c_{2}=a_{2}+b_{2}+c_{2}+2ab+2bc+2ca$
 $(a−b−c_{2}=a_{2}+b_{2}+c_{2}−2ab−2bc+2ca$
बीजगणित सूत्र घन:
 $(a+b_{3}=a_{3}+3a_{2}b+3ab_{2}+b_{3}$
 $(a+b_{3}=a_{3}+b_{3}+3ab(a+b)$
 $(a−b_{3}=a_{3}−3a_{2}b+3ab_{2}−b_{3}$
 $(a−b_{3}=a_{3}−b_{3}−3ab(a−b)$
 $a_{3}−b_{3}=(a−b)(a_{2}+ab+b_{2})$
 $a_{3}+b_{3}=(a+b)(a_{2}−ab+b_{2})$
और कुछ अतिरिक्त बीजगणित सूत्र:
 $(a+b_{4}=a_{4}+4a_{3}b+6a_{2}b_{2}+4ab_{3}+b_{4}$
 $(a−b_{4}=a_{4}−4a_{3}b+6a_{2}b_{2}−4ab_{3}+b_{4}$
 $a_{4}−b_{4}=(a−b)(a+b)(a_{2}+b_{2})$
 $a_{5}−b_{5}=(a−b)(a_{4}+a_{3}b+a_{2}b_{2}+ab_{3}+b_{4})$
Frequently Asked Questions

What is the algebraic formula for a+b whole cube?
 The formula for $(a+b_{3}$ is $a_{3}+3a_{2}b+3ab_{2}+b_{3}$.

How can I derive the formula for a+b whole cube?
 The formula can be derived by expanding $(a+b)(a+b)(a+b)$ using the distributive property and combining like terms.

What is the simplified form of a+b whole cube?
 The simplified form of $(a+b_{3}$ is $a_{3}+3a_{2}b+3ab_{2}+b_{3}$.

Is there an alternative way to express a+b whole cube?
 Yes, $(a+b_{3}$ can also be expressed as $a_{3}+b_{3}+3ab(a+b)$.

Can the formula a+b whole cube be used for negative numbers a+b whole cube?
 Yes, the formula is valid for any real numbers $a$ and $b$, including negative numbers.

Where can I find a PDF containing all algebraic identity formul as a+b whole cube ?
 You can find PDFs of algebraic identity formulas on educational websites, online libraries, and mathematics resource sites.

How can I access a chart of all algebraic identities a+b whole cube ?
 Charts of algebraic identities are often available in textbooks, online educational platforms, and downloadable resources from academic websites.

Are there any apps that provide a list of algebraic formulas a+b whole cube?
 Yes, several educational apps provide comprehensive lists of algebraic formulas, including Khan Academy, Wolfram Alpha, and Photomath.

What is the importance of knowing algebraic identities like a+b whole cube?
 Knowing algebraic identities helps simplify complex expressions, solve algebraic equations, and understand the properties of polynomials.

Can I get a list of algebraic identities formulas in Hindi a+b whole cube?
 Yes, many educational websites and resources offer algebraic identities formulas in Hindi. You can search for them online or check local educational platforms.
conclusion
Ranjay, hailing from Bihar, holds a Bachelor’s degree in Journalism from Patna University. Boasting three years of practical experience in journalism, he injects a unique and perceptive outlook into his endeavors. Ranjay’s fervor for storytelling is evident, drawing inspiration from his Bihar heritage.