Question

If a-b=7 and a²+b²=85 find a³-b³=?

Answer 1

$(a - b) {}^{2} = a {}^{2} + {b}^{2} - 2ab \\ {7}^{2} = 85 - 2ab \\ 49 = 85 - 2ab \\ 2ab = 85 - 49 \\ 2ab = 34 \\ ab = 17 \\ \\ {a}^{3} - {b}^{3} = ( a - b)( {a}^{2} + ab + {b}^{2} ) \\ \: \: \: \: \: \: \: \: \: \: \: = 7(85 + 17) \\ \: \: \: \: \: \: \: \: \: \: \: = 7 \times 102 = 714$