Factor
\left(y-1\right)\left(y^{2}+y+1\right)\left(y^{6}+y^{3}+1\right)
Evaluate
y^{9}-1
Graph
Share
Copied to clipboard
\left(y^{3}-1\right)\left(y^{6}+y^{3}+1\right)
Rewrite y^{9}-1 as \left(y^{3}\right)^{3}-1^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).
\left(y-1\right)\left(y^{2}+y+1\right)
Consider y^{3}-1. Rewrite y^{3}-1 as y^{3}-1^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).
\left(y-1\right)\left(y^{2}+y+1\right)\left(y^{6}+y^{3}+1\right)
Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: y^{2}+y+1,y^{6}+y^{3}+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}