Question

Simplify: (x3-y3)3+(y3-z3)3+(z3-x3) 3 divided by (x-y)3+(y-z)3+(z-x)3

Answer 1

$\frac{ { ({x}^{3} - {y}^{3}) }^{3} + {( {y}^{3} - {z}^{3} )}^{3} + {( {z}^{3} - {x}^{3} )}^{3} }{ {(x - y)}^{3} + {(y - z)}^{3} + {(z - x)}^{3} } \\ = \frac{3( {x}^{3} - {y}^{3})( {y}^{3} - {z}^{3})( {z}^{3} - {x}^{3})}{3(x - y)(y - z)(z - x)} \\ = (x - y)( {x}^{2} + {y}^{2} + xy)(y - z)( {y }^{2} + {z}^{2} + yz)(z - x)( {z}^{2} + {x}^{2} + zx) \div (x - y)(y - z)( z- x) \\ = ( {x}^{2} + {y}^{2} + xy)( {y}^{2} + {z}^{2} + yz )( {z}^{2} + {x}^{2} + x z ) \\ using \\ if \: a + b + c = 0 \\ then\\ {a}^{3} + {b}^{3} + {c}^{3} = 3abc \:$

Answer 2

Step-by-step explanation:

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