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Algebra Formulas, All Algebraic Identities Formulas PDF, Formula Chart, List

Algebra is a branch of Mathematics that substitutes letters for numbers. An algebraic equation depicts a scale, what is done on one side of the scale with a number is also done on either side of the scale. Mathematical numbers are constants. Algebra also includes real numbers, complex numbers, matrices, vectors, and much more. X, Y, A, and B are the most commonly used letters that represent algebraic problems and equations.

Algebra Formula

“Algebra Formulas form the foundation of numerous most important topics of mathematics. Topics like equations, quadratic equations, polynomials, coordinate geometry, calculus, trigonometry, and probability, extensively depend on algebra formulas for understanding and for solving complex problems.”

Algebra Formula Definition

The Algebra formula is part of Class 10 in India. One of the most crucial areas of mathematics is algebra. Numerous disciplines, including quadratic equations, polynomials, coordinate geometry, calculus, trigonometry, probability, and others, can be solved using algebraic formulas. In Algebra formulas, we used numbers along with letters together. The most common letters used in algebraic equations and problems are X, Y, A, and B. These Algebra formulas enable us to quickly and efficiently tackle time-consuming algebraic problems. Here, we include all significant Algebra formulas together with their solutions, so that students can access them all in one place.

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Algebra Formulas

Algebra formulas are basically algebra equations formed by algebraic and mathematical phrases and symbols. These algebraic formulas contain an unknown variable x which can be generated while simplifying an equation. These algebraic equations solve complicated algebraic computations in an easy way.
For Algebra formulas example,

(a+b)³ =a³+ 3a²b+3ab²+b³
In the above Algebra formulas, both sides are individually an algebraic equation. Where ( a³ + 3a²b+3ab²+b³ ) is the simplified expression of (a+b)³ .

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Algebra Formulas Identities

In algebra formulas, an identity is an equation that is always fall true regardless of the values assigned to the variables. Algebraic Identity means that the left-hand side (LHS) of the equation is identical to the right-hand side (RHS) of the equation and for all values of the variables. Algebraic identities applications are in solving the values of unknown variables. Here are some commonly used algebraic identities:

Algebraic Identities Formula

  • (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

Algebra Formulas Square for Class 10

Here are some Algebra formulas involving squares.
• 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 + 2bc + 2ca
• (a – b – c)² = a²+ b²+ c²– 2ab + 2bc – 2ca

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Algebra Formulas Cube for SSC CGL

Here are some Algebra 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)

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Algebra Formulas- Natural Numbers

Algebra formulas for Natural Numbers Except for 0 and negative numbers , the rest of the numbers [ 2 to infinity] in the number system that humans can count are known as Natural Numbrrs. Some algebraic formulas are applied when performing operations on natural numbers. They are.
Consider n to be a natural number.

  1. (an – bn )= (a – b)(an-1 + an-2b+…+ bn-2a + bn-1)
  2. ( an + bn)= (a + b)(an-1 – an-2b +…+ bn-2a – bn-1) [ where n is even  , (n = k + 1)  ]
  3. (an + bn )= (a + b)(an-1 – an-2b +an-3b2…- bn-2a + bn-1) [ where n is odd , (n = 2k + 1)  ]

Algebraic Formulas- Laws of Exponents 

In Algebra formulas An Exponent or power is used to demonstrate the repeated multiplication of a number. Such as 3×3×3×3 can be written as 3⁴ where 4 is the exponent of 3.   In general, exponents or powers indicate how many times a number can be multiplied. There are various rules to operate an exponent for addition, subtraction, and multiplication which are easily solved by algebraic formulas.

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Algebra formula: Laws of Exponents

Algebra Formulas- Quadric equations

Algebra formulas for Quadric equations are one of the most important topics in the syllabus of Class 9 and 10 . To find the root of the given  quadric equations we used the following Algebra formulas

If ax²+bx+c =0 is a quadric equation ,then

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Algrabra formula :Quadric equations

 

From the above formula we can conclude that , If the roots of the quadric equation are α and β
1. The equation will be (x − α)(x − β) = 0,
2.  The value of (α + β ) = (-b / a) and α × β = (c / a).

Algebra Formulas For Irrational Numbers (SSC CGL)

The Algebra formulas used to solve equations based on Irrational Numbers are following

  1. √ab = √a √b
  2. √a/b =√a / √b
  3. ( √a +√b )  ( √a – √b ) = a-b
  4. ( √a +√b )²= a + 2 √ab + b
  5. ( a +√b )( a -√b )= a² – b

Algebra Formulas List and Sheet

Here a list of all important Algebra formulas is provided. Students must go through the list to solve difficult algebraic equations very quickly.

 

Important Algebra 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)

Algebraic Formulas PDF

Check Out The Algebra Formulas PDF for Class 10 Students. Click Here- Algebra formulas

Algerbra Formula chart

Algerbra Formula Chart is Given Below, Check Now.

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Algerbra Formula Chart

a+b+c Whole Square Formula- (a+b+c)^2 Formula

The square of the sum of three terms, , can be expanded using the formula for the square of a trinomial:

So, is equal to the sum of the squares of the individual terms (, , ) and twice the products of the pairs of terms (, , ).

This expansion holds true for any values of , , and .

a-b Whole Square

The square of the difference between two terms, , can be expanded using the formula for the square of a binomial:

So, is equal to the square of the first term (), minus twice the product of the two terms (), and the square of the second term ().

This expansion holds true for any values of and .

a+b Whole Square

The square of the sum of two terms, , can be expanded using the formula for the square of a binomial:

So, is equal to the sum of the squares of the individual terms ( and ) and twice the product of the terms ().

This expansion holds true for any values of a and .

Algebraic Formulas with Examples (solved)

Example 1 : Find the value 20²- 15²
Solution: To solve the  equation ,the formula we use is
a² -b² = (a+b) (a-b)
= (20+15)(20-15)
= 35 × 5
= 175 (Answer)

Example 2 : (x-y) =2 and x²+ y² =20 then find the value of x  and y [ where x,y >0 ]
Solution: Here , x²+ y² =20
(x-y)² +2xy =20
Or, (2)²+ 2xy =20
Or, 2xy = 20-4  = 16
Or,xy = 8
Now, (x+y)²= (x-y)² +4xy = (2)² +4.8 =36
Or,x+y = ± 6
So, x+y = 6 [x,y >0 ] ….(1)
We also get , x- y =2 ……(2)
Solving two equations we get ,
x = 4 and y = 2 (Answer)

Example 3 : Divide( a³ + b³ + c³ – 3abc )by( a+b+c )and the quotient.Determine the magnitude.

Solution: a+b³ + c3 – 3abc

=(a+b+c)(a²+b²+c2-ab-ac-bc)

Determinant quotient =
[(a+b+c)(a²+b²+c²-ab-ac-bc)] ÷ (a+b+c)

= a²+b²+c²-ab-be-ca.

Magnitude of quotient is  2. (Answer)

Example 4
Find their successive product (x + y), (x – y),  (x² + y²).

Solution :Determinant serial product =
(x + y) (x – y) (x² + y²)
= (x²-y²)(x² + y²)
= (x²)² – (y²)²
= x⁴ – y ⁴.( Answer)

Algebraic formulas- Questions

1. If x+y = 3 and xy = 2, what is the value of (x – y) ² ?
2. If a+b = 8 and ab = 15, what will be the values ​​of a and b?
3. If a+b = 5 and ab = 6, Find the value of a² – b² ?
4. If x = 29 and y = 14, what is the value of (4x² + 9y²+ 12xy )?

Algebraic Identities Formulas in Hindi

बीजगणित सूत्र कक्षा 10  के लिए 

यहां कुछ बीजगणित सूत्र दिए गए हैं जिनमें वर्ग शामिल हैं।
• a²– b² = (a – b)(a + b)
• (a + b)²=  a²+ 2ab + b²
• a²+ b²= (a + b)²– 2ab
• (ए – बी)² = ए²– 2ab+ बी²
• (a + b + c)² = a² + b² + c²+ 2ab + 2bc + 2ca
• (ए – बी – सी)² = ए²+ बी²+ सी²-2ab + 2bc – 2ca

एसएससी सीजीएल के लिए बीजगणित सूत्र

यहाँ कुछ बीजगणित सूत्र दिए गए हैं जिनमें घन शामिल हैं।

• (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)

कुछ और बीजगणित सूत्र हैं –
• (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)

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Algebraic Formulas- QNA

Q, What are formula used to solve algebra problems ? 

Mainalgebra  formulas which are widely used are

• 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 + 2bc + 2ca

•(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)

Q. What are the formulas used to solve equation based on Irrational Numbers?

The formulas used to solve equation based on Irrational Numbers are following

  1. √ab = √a √b
  2. √a/b =√a / √b
  3. ( √a +√b )  ( √a – √b ) = a-b
  4. ( √a +√b )²= a + 2 √ab + b
  5. ( a +√b )( a -√b )= a² – b

Q. Write down the simplified form of ( a+b)² .

The simplified form of ( a+b)² is  (a²+ 2ab + b²)

 

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FAQs

What are formula used to solve algebra problems ? 

Main algebra  formulas which are widely used are 
• 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 + 2bc + 2ca
•(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

What are the formulas used to solve equation based on Irrational Numbers?

The formulas used to solve equation based on Irrational Numbers are following 
√ab = √a √b
√a/b =√a / √b
( √a +√b )  ( √a - √b ) = a-b
( √a +√b )²= a + 2 √ab + b 
( a +√b )( a -√b )= a² - b

Write down the simplified form of ( a+b)² .

The simplified form of ( a+b)² is  (a²+ 2ab + b²)

How to find the expansion of higher power powers in algebra?

The expansion of higher order powers in algebra is found using the concept of binomial theorem.

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