Question

11. Упростите: a²(a-b) + 3 a³-b³ b² + ab 2 a² + àb + b² a+2b a - ? -​

Answer 1

$\frac{ {a}^{2}(a - b) }{ {a}^{3} - b {}^{3} } + \frac{b {}^{2} + ab }{ {a}^{2} + ab + {b}^{2} } = \frac{ {a}^{2}(a - b) }{(a - b)(a {}^{2} + ab + b {}^{2}) } + \frac{ {b}^{2} + ab }{a {}^{2} + ab + b {}^{2} } = \\ = \frac{ {a}^{3} - {a}^{2} b + (a - b)(b {}^{2} + ab) }{(a - b)( {a}^{2} + ab + {b}^{2} } = \frac{ {a}^{3} - {a}^{2}b + a {b}^{2} + {a}^{2} b - {b}^{3} - a {b}^{2} }{ {a}^{3} - b {}^{3} } = \\ = \frac{ {a}^{3} - b {}^{3} }{ {a}^{3} - {b}^{3} } = 1$