Question

verify x³+y³=(x+y)(x²-xy+y²)
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Answer 1

Answer:

Taking RHS,

$= (x + y)( {x}^{2} - xy + {y}^{2}$)

$= x( {x}^{2} - xy + {y}^{2} ) + y( {x}^{2} - xy + {y}^{2} )$

$= {x}^{3} - {x}^{2}y + x {y}^{2} + \\ {x}^{2}y - x {y}^{2} + {y}^{3}$

The numbers which are same but have different signs will be cancelled .

$= {x}^{3} + {y}^{3}$

Hence,

${x}^{3} + {y}^{3 } = {x}^{3} + {y}^{3}$

LHS= RHS

hence proved!!