Factor
\left(x+y\right)\left(x^{2}-xy+y^{2}-1\right)
Evaluate
x^{3}-x+y^{3}-y
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x^{3}-x-y+y^{3}
Consider x^{3}-x-y+y^{3} as a polynomial over variable x.
\left(x+y\right)\left(x^{2}-xy+y^{2}-1\right)
Find one factor of the form x^{k}+m, where x^{k} divides the monomial with the highest power x^{3} and m divides the constant factor y^{3}-y. One such factor is x+y. Factor the polynomial by dividing it by this factor.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
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Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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