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

r2 s2 + 2st t2

= r2 − (s2 − 2st + t2)

We recognize that s2 − 2st + t2 is a square, and equals (st)2. So we can factor our expression as follows:

r2 s2 + 2st t2

= r2 − (s2 − 2st + t2)

= r2 − (st)2

[This is also a difference of 2 squares.]

= [r − (st)][r + (st)]

= (rs + t)(r + st)

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