Question

What should be subtracted from x3+y3 to obtain x2 + y2 ?

Answer 1

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Answer 2

$x {}^{3} + y {}^{3} - (x {}^{3} + y {}^{3} - x {}^{2} - y {}^{2} ) \\ \\ = x {}^{3} + y {}^{3} - {x}^{3} - y {}^{3} + {x}^{2} + y {}^{2} \\ \\ = x {}^{2} + y {}^{2} \\ \\ hence \: we \: must \: subtract \: (x {}^{ 3 } + y {}^{3} - x {}^{2} - y {}^{2} ) \: from \: x {}^{3} + y {}^{3} \: to \: obtain \: {x}^{2} + {y}^{2} .$

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