Factor
y\left(y^{2}+1\right)\left(y^{4}-y^{2}+1\right)
Evaluate
y^{7}+y
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y\left(y^{6}+1\right)
Factor out y.
\left(y^{2}+1\right)\left(y^{4}-y^{2}+1\right)
Consider y^{6}+1. Rewrite y^{6}+1 as \left(y^{2}\right)^{3}+1^{3}. The sum of cubes can be factored using the rule: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).
y\left(y^{2}+1\right)\left(y^{4}-y^{2}+1\right)
Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: y^{4}-y^{2}+1,y^{2}+1.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
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
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}