Question

(a+b)³ + (b+c)³ + (c+a )³ -3 (a+b)(b+c) (c+a)=2(a³+b³+c³) prove it.
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Answer 1

$</p><p></p><p></p><p>------------------------------------------------------------------------------------------------------------------------------------------</p><p></p><p>Identity to use : (a-b)² = a² - 2ab + b²</p><p></p><p>________________________________</p><p></p><p></p><p></p><p>----------------------------------------------------------------------------------------------------------------------------------------------</p><p></p><p>Some more identities : Extras</p><p></p><p>a²-b² = (a+b)(a-b)</p><p></p><p>(x+a)(x+b) = x² + x(a+b) + ab</p><p></p><p>(a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ca</p><p></p><p>(a+b)³ = a³ + 3a²b + 3ab² + b³</p><p></p><p>(a-b)³ = a³ - 3a²b + 3ab² - b³</p><p></p><p>a³ - b³ = (a-b)(a²+ab+b²)</p><p></p><p>a³ + b³ = (a+b)(a²-ab+b²)</p><p></p><p>a³ + b³ + c³ = (a+b+c)(a²+b²+c²-ab-bc-ca)</p><p></p><p>Conditional identity:</p><p></p><p>if a+b+c = 0,</p><p></p><p>a³ + b³ + c³ = 3abc</p><p></p><p>_________________________________________</p><p></p><p>$