Question

a³-b³ . (a+b+a-b): a²+ab+b²=?
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2a+2b (a-b+a+b) : a²-b² =?

Answer 1

$frac{ {a}^{3} - {b}^{3} }{2a + 2b} times frac{(a + b + a - b)}{(a - b + a + b)} div frac{ {a}^{2} + ab + {b}^{2} }{ {a}^{2} - {b}^{2} } = frac{ ({a}^{3} - {b}^{3}) times (a - b + a + b) times (a + b)(a - b) }{2(a + b) times (a - b + a + b) times ({a}^{2} + ab + {b}^{2}) } = frac{(a - b)( {a}^{2} + ab + {b}^{2}) times (a - b)}{2 times ( {a}^{2} + ab + {b}^{2}) } = frac{(a - b) times (a - b)}{2} = frac{ {(a - b})^{2} }{2} = frac{ {a}^{2} - 2ab + {b}^{2} }{2}$