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The 'difference of two squares' is a key algebraic transformation and problems like this can lead students into a deeper appreciation of that form through a further visualisation.
The problem of writing the number $105$ as the difference of two squares becomes a problem about factor pairs that make a product of $105$.
Draw out from the students how this transformation helps [we now seek factors of $105$ rather than guessing squares and calculating differences].
For $105$ (and then for $1155$) how many ways might there be, and why do you think that ?