If (a - b) = 12 and (a² + b²) = 170, find (a³-b³).
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2196
Given a-b=12
squaring on both sides
a²+b²-2ab=144
we have a²+b²=170
so
170-2ab=144
2ab=26
ab=13
a³-b³=(a-b)(a²+ab+b²)
a³-b³=12(170+13)
=12(183)
a³-b³=2196
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