2.(i)  Evaluate the following product without multiplying directly:

   (i)    103 \times 107

Answers (1)

We can rewrite  103 \times 107  as 

\Rightarrow 103 \times 107= (100+3)\times (100+7)

We will use identity

(x+a)(x+b)=x^2+(a+b)x+ab

Put  x =100 , a=3 \ \ and \ \ b = 7

(100+3)\times (100+7)= (100)^2+(3+7)100+3\times 7

                                               =10000+1000+21= 11021

Therefore, value of 103 \times 107  is  11021

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