We recognize that this involves 2 differences of two squares. We group it as follows:

*r*^{2}* *− *s*^{2 }+ 2*st ** *− *t*^{2}

= *r*^{2}* *− (*s*^{2 }− 2*st *+ *t*^{2})

We recognize that *s*^{2 }− 2*st *+ *t*^{2} is a square, and equals (*s* − *t*)^{2}. So we can factor our expression as follows:

*r*^{2}* *− *s*^{2 }+ 2*st ** *− *t*^{2}

= *r*^{2}* *− (*s*^{2 }− 2*st *+ *t*^{2})

= *r*^{2}* *− (*s* − *t*)^{2}

[This is also a difference of 2 squares.]

= [*r* − (*s* − *t*)][*r* + (*s* − *t*)]

= (*r* − *s* + *t*)(*r* + *s* − *t*)

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