Answer
$1-20a+100a^2$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the given expression, $
(1-10a)^2
$, is equivalent to
\begin{array}{l}\require{cancel}
(1)^2+2(1)(-10a)+(-10a)^2
\\\\=
1-20a+100a^2
.\end{array}