Algebra Formulas | Basic Algebraic Formulas in Mathematics

 What is Algebra?

Algebra is the main and broad parts of the Mathematics subject. It is one of the most important study of mathematical symbols and the rules for manipulating those symbols. It includes elementary equations. Algebra includes arithmetic operations such as addition, subtraction, multiplication and division which help us to solve mathematical problems. Algebra deals with variables, constants and arithmetic operations.

Algebra Formulas  Basic Algebraic Formulas in Mathematics

In algebra, an equation is a mathematical sentence with an equal sign.

Example:  2 + 5 = 7

                  8 – 2 = 6
                  3 × 2 = 6
                  10 ÷ 2 = 5

Here you can find some formulas of algebra.

Some Important Formulas in Algebra

Here is a list of Some Algebraic formulas –

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

(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)

Solved Example:-

Question: Find out the value of 5² – 3²

Solution:
Using the formula of a² – b² = (a – b)(a + b)
              where a = 5 and b = 3
 Now, (a – b)(a + b)
        = (5 – 3)(5 + 3)
        = 2 × 8
        = 16