Factorise a-b-a 3 +b 3
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a-b-a³+b³
=a-b-(a³-b³)
=(a-b)-{(a-b)³+3ab(a-b)}
=(a-b){1-(a-b)²+3ab}
=(a-b){1-(a²-2ab+b²)+3ab}
=(a-b)(1-a²+2ab-b²+3ab)
=(a-b)(1-a²-b²+5ab)
=a-b-(a³-b³)
=(a-b)-{(a-b)³+3ab(a-b)}
=(a-b){1-(a-b)²+3ab}
=(a-b){1-(a²-2ab+b²)+3ab}
=(a-b)(1-a²+2ab-b²+3ab)
=(a-b)(1-a²-b²+5ab)
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