Answer
$10,404$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
102^2
,$ use the special product for the square of a binomial.
$\bf{\text{Solution Details:}}$
Since $102$ is near the number $100$ (a number that is convenient to operate with because it has many zeros), the given expression can be expressed as $
(100+2)^2
.$ Using the square of a binomial which is given by $(a+b)^2=a^2+2ab+b^2$ or by $(a-b)^2=a^2-2ab+b^2,$ then $(100+2)^2$ is equivalent to
\begin{array}{l}\require{cancel}
(100)^2+2(100)(2)+(2)^2
\\\\=
10000+400+4
\\\\=
10,404
.\end{array}
