Question

Evaluate the product $103\times 107$ without multiplying directly

Answer 1

Given expression can be written as

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

We know that

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

Here $x=100,a=3,b=7$

$$\begin{gathered} \Rightarrow (100+3)\times (100+7)] \\ ={\left(100\right)}^2+(3+7)\times 100+(3\times 7) \\ =10000+1000+21 \\ =11021 \end{gathered}$$

Hence the product is $11021$