We recognise that this involves 2 differences of two squares. We group it as follows:
r2 − s2 + 2st − t2 = r2 − (s2 − 2st + t2)
We recognise that s2 − 2st + t2 is a square, and equals (s − t)2. So we can factor our expression as follows:
r2 − s2 + 2st − t2 |
= r2 − (s2 − 2st + t2) = r2 − (s − t)2 [This is also a difference of 2 squares.] = [r − (s − t)][r + (s − t)] = (r − s + t)(r + s − t) |