Question

If a-b=-8 & ab=21 than a³-b³=

Answer 1

Answer

1016

Steps

$a - b = 8 \\ ab = 21$

To find

${a}^{3} - {b}^{3}$

Using formula

${a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} ) \\ = 8 \times ( {a}^{2} + 21 + {b}^{2} ) \\ = 8({a}^{2} + {b}^{2} + 21 ) \\ using \: {a}^{2} + {b}^{2} = {(a - b)}^{2} + 2ab \\ \\ = 8( {(a - b)}^{2} + 2ab + 21 ) \\ = 8( {(8)}^{2} + 2 \times 21 + 21 ) \\ = 8( 64 + 42 + 21 ) \\ = 8 \times 127 \\ = 1016$