Answer
$9,999$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
99\times101
,$ get the middle number between $99$ and $101$. Then use the special product for the sum and difference of like terms.
$\bf{\text{Solution Details:}}$
The middle number between $99$ and $101$ is $100.$ Using the product of the sum and difference of like terms which is given by $(a+b)(a-b)=a^2-b^2,$ the expression above is equivalent\begin{array}{l}\require{cancel}
(100-1)(100+1)
\\\\=
(100)^2-(1)^2
\\\\=
10000-1
\\\\=
9,999
.\end{array}
