Answer
$8\left( r-\dfrac {3y}{16}\right) ^{2}+\dfrac {311y^{2}}{32}$
Work Step by Step
$8r^{2}-3rs+10s^{2}=8\left( r^{2}-\dfrac {3}{8}rs+\dfrac {9y^{2}}{256}\right) +\dfrac {311y^{2}}{32}=8\left( r-\dfrac {3y}{16}\right) ^{2}+\dfrac {311y^{2}}{32}$
