Know your tricks

A trick to solve the $xy5^2$ $(1)$ is to write $25$ at the end of the result. $xy \times (xy+1)$ is the first 2 digits:

$105^2=(10\times11) 25=11025$

$115^2=(11\times12) 25 = 13225$

$125^2=(12\times13) 25=15625$

Wow! If we add them together, $1$ is as same as $2$ . Therefore:

$(1)+(2)=2\times(11025+13225+15625)=2\times39875=\boxed{79750}$