Answer
$x^{2}+4y^{2}-4xy-2x+4y+1$
Work Step by Step
$(x-2y-1)^{2}=(x-2y-1)(x-2y-1)$
... distribute (multiply horizontally)
$=x(x-2y-1)-2y(x-2y-1)-(x-2y-1)$
... distribute each parentheses
$=x^{2}-2xy-x-2xy+4y^{2}+2y-x+2y+1$
... add like terms, write in descending order of exponents
= $x^{2}+4y^{2}-4xy-2x+4y+1$
