Question

Find the product using identities : 105 x 97.

Answer 1

Hi,friend 
For this Problem we will use an Identity that,
(x+a) (x+b) = x²+x(a+b) + ab.
Now we can write 105 as (100+5) and also 97 as (100-3).
Therefore here,
      x= 100, a= 5 and b= -3
now by putting these values in the above Algebraic Identity we get,
  {100+5} {100+(-3)} = 100²+100(5-3)+5×(-3)
                             = 10000+500-300-15
                             = 10185
Hence, 105×97 = 10185

Answer 2

Answer:

Step-by-step explanation:

Hi,friend  

For this Problem we will use an Identity that,

(x+a) (x+b) = x²+x(a+b) + ab.

Now we can write 105 as (100+5) and also 97 as (100-3).

Therefore here,

     x= 100, a= 5 and b= -3

now by putting these values in the above Algebraic Identity we get,

 {100+5} {100+(-3)} = 100²+100(5-3)+5×(-3)

                            = 10000+500-300-15

                            = 10185

Hence, 105×97 = 10185