(x² -xy + y²) * (x² +xy - y²) - x *(x-y)³ -3xy * (x² + y²)=

asked by guest
on Dec 28, 2024 at 9:21 am



You asked:

Evaluate the expression: \(\left({x}^{2} - x y + {y}^{2}\right) \left({x}^{2} + x y - {y}^{2}\right) - x {\left( x - y \right)}^{3} - 3 x y \left({x}^{2} + {y}^{2}\right)\)

MathBot Answer:

Evaluated



\(\displaystyle \left({x}^{2} - x y + {y}^{2}\right) \left({x}^{2} + x y - {y}^{2}\right) - x {\left( x - y \right)}^{3} - 3 x y \left({x}^{2} + {y}^{2}\right) = - 3 x y \left(x^{2} + y^{2}\right) - x \left(x - y\right)^{3} + \left(x^{2} - x y + y^{2}\right) \left(x^{2} + x y - y^{2}\right) \)

Expanded

\[\left({x}^{2} - x y + {y}^{2}\right) \left({x}^{2} + x y - {y}^{2}\right) - x {\left( x - y \right)}^{3} - 3 x y \left({x}^{2} + {y}^{2}\right) = - 4 x^{2} y^{2} - y^{4}\]

Factored

\[\left({x}^{2} - x y + {y}^{2}\right) \left({x}^{2} + x y - {y}^{2}\right) - x {\left( x - y \right)}^{3} - 3 x y \left({x}^{2} + {y}^{2}\right) = - y^{2} \cdot \left(4 x^{2} + y^{2}\right)\]

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