Learn Algebra Formula

Learn Algebra Formula 

Learn Algebra Formula
Learn Algebra Formula 

algebra is the study of mathematical symbols and the rules for manipulating these symbols. And
we know the formula is the mathematical relationship or rule expressed in symbols. Algebra is based on solving the equation of variables and constants and deriving the values ​​of variables. Here we will derive the algebra formulas and this is tricks u can use to remember the formula or u can derive algebra formulas on your own .No need to remember formulas, only understand how it is derived. Automatically u can do it on your own.

Learn How algebra formulas are derived

1.(a-b) 2 = (a-b) (a-b)

         = a. a- a. b- b. a+ b .b

        = a2-ab-ba+b2

           = a2-2ab+b2

2.(a + b) 2 = (a+ b) (a+ b)

             = a. a+ a. b + b. a+ b .b

             = a2+ab+ba+b2

             = a2+2ab+b2

3.     3.(a+ b)2-2ab = a2+b2


      {(a+ b) (a+ b)}-2ab                       ———left side of equal symbol

     {( a. a+ a. b+ b .a + b .b)}-2ab


    (a2+2ab+ b2)-2ab

   a2+2ab+ b2-2ab                                 —–open the bracket


3.      4.   (a-b)(a +b) = a2– b2

(a- b)(a +b)                              ———left side of equal symbol          

a.     a+ a. b -b. a-b. b

a2+ab-ab-b2                           —- +ab and –ab cancelled

a2– b2

3.      5. (a+ b+ c)2 = a2+b2+c2+2ab+2bc+2ac

     ( a+ b+ c) ( a+ b+ c)                             —- left side of equal symbol

    (a .a +a .b +a .c +b. a+ b .b+ b .c+ c .a +c .b  +c .c)

    a2+ab+ac+ba+b2+ bc+ca+cb+c2

     a2+b2+c2+2ab+2bc+2ca                    — ab= ba ,  bc = cb and ca =ac

3.    6.(a-b-c)2=a2+b2+c2-2ab+2bc-2ac

              (a-b-c)2 = (a-b-c)(a-b-c)                    —we can write like this.

              =(a. a- a. b-a. c-b. a+ b. b +b .c – c .a+ c .b + c .c


             =a2+b2+c2-2ab+2bc-2ac         —our formula

7.    (a+ b)3= (a+ b)(a+ b)(a+ b)

                  = {(a+ b) (a+ b)} (a+ b) 

                  = (a. a+ a. b+ b. a+ b. b) (a+ b)

                  = (a2 + ab+ba+b2) (a + b)

                   = (a2+2ab+b2) (a +b)

                   = a2.a+a2.b+2ab.a+2ab.b+b2.a+b2.b

                   = a3+a2b+2a2b+2ab2+b2a+b3

                  = a3+3a2b+3ab2+b3        ———our formula

following this we can derive all the formulas of algebra.

Algebraic Expressions:- 

 1. 2x means x + x, i.e. double of x. Broadly, if m is a positive whole number, then mx      means   m times the x. mx is also called the product of m and x.

    2.        X2means x .x;
          x3 means x. x .x.
     Broadly, if m is a positive whole number then xm means  x .x .x  ….. m times.

In x m, m is called exponent and x is called base. Later, the meanings of mx and xm are expanded and are also given in those situations when m is any number of minus, different, irrational etc.

Laws of Exponents: 

1.(x)m .(x)=(x)m+ n

2. (x)m/(x)=(x)m- n

3(x y)m= x y m

4. (x m)= x m n

Basic rules and properties of Algebra. 


(1) Closure: If a set has two elements x and y, then x * y is also an element of the same set.

(2) Commutativity:  x * y = y * x

(3) Associativity: If x, y, z are components of a set, then (x * y) * z = x * (y * z)

4) Existence of identity: The set must have such a component that a * e = e * a = a

(5) Existence of inverse: In a set, any element corresponding to any component a has a-1 such that a * a-1 = a-1 * a = e

(6) Distribution rules against first operation and second operation: x (y * z) = (x y) * (x z) and (y* z) x = (y x) * (z x)

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Solved Questions
 1.Give basic formula in algebra arithmetic
  •         (a + b)2 = a2 + 2ab + b2   
  •           (a – b)2 = a2 – 2ab +b2  
  •         a2 b2=(a + b)(a – b)

  •        (a+ b)3 = a3 + 3a2b + 3ab2 + b3

  •        (a-b)3=a3-3a2b+3ab2-b3

  •          a3+b3=(a+ b)(a2+ab+b2)

  •         (a+ b+ c)2 = a2+b2+c2+2ab+2bc+2ac

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