## College Algebra (11th Edition)

$10,404$
$\bf{\text{Solution Outline:}}$ 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}