Question

21. (a' - b') = (a - b) ((a - b)² + 3ab)​

Answer 1

(a'- b') = (a - b) ((a - b)²+3ab)

$= (a - b)( {a}^{2} + {b}^{2} - 2ab + 3ab) \\ = (a - b)({a}^{2} + {b}^{2} + ab) \\ = a({a}^{2} + {b}^{2}+ ab) - b({a}^{2} + {b}^{2}+ab) \\ = {a}^{3} + ab {}^{2} + {a}^{2} b - {a}^{2} b - {b}^{3} - ab {}^{2} \\ = {a}^{3} - b {}^{3}$