Answer
$5,041$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
71^2
,$ use the special product for the square of a binomial.
$\bf{\text{Solution Details:}}$
Since $71$ is near the number $70$ (a number that is convenient to operate with because of the zero), the given expression can be expressed as $
(70+1)^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 $(70+1)^2$ is equivalent to
\begin{array}{l}\require{cancel}
(70)^2+2(70)(1)+(1)^2
\\\\=
4900^2+140+1
\\\\=
5,041
.\end{array}
