Question

6. Simplify (x2 + xy + y²)(x - y) and verify the result for x =4
.=-3 please tell the answer​

Answer 1

Explanation:

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

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

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

${x}^{3} - {y}^{3}$

$for \: x = 4 \: \: and \: \: y = - 3$

LHS :

$( {4}^{2} + 4 \times - 3 + ( { - 3}^{2} ))(4 - ( - 3))$

$(16 - 12 + 9)(7)$

$(13)(7)$

$91$

RHS :

${4}^{3} - ( { - 3}^{3} )$

$64 - ( - 27)$

$64 + 27$

$91$

Hence proved...

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