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Algebraic Identities: Identities I-IV

Identity I:

Identity II:

Identity III:

Identity IV:
 

Example :

Find the following products using identities

  (a)

  (b)

  (c)

 (d) 95´ 105

Solution :

(a)

Using the Identity I: , here,

                             

                                        = + 10 + 25

(b)

Using the identity IV:

Here,

 

=++ 3

× 4

                = +7+12

(c)

Using the Identity II:

Here

= - 2

× 7 × x + 7 × 7

         = - 14x + 49

(d) 95 × 105

 

Using the identity

Here

 

        

 

We can also use the identities to factorize the given polynomial. In the following

examples we are going to see how to factorize the polynomial using identities.

 

Example : Factorize
 

=48xy=2× 6× 4

xy 9;

= +2× 6× 4xy+

Using the Identity I : ,

We have, = = (6x+4y)´ (6x+4y)

 

Example : Factorize
 

                =

 

Using the identity ,

                 x=3x, y=4y

                =

                            = (3x+4y)× (3x-4y)

 

Example : Factorize:

Let x = 2x;  t = y + z

Using the Identity I: ,

=

               =

Substituting the value of t,

=

              =

              =


 



 


 




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