Factor
\frac{\left(3x-1\right)\left(3x+1\right)\left(-9x^{2}-1\right)}{81}
Evaluate
\frac{1}{81}-x^{4}
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\frac{1-81x^{4}}{81}
Factor out \frac{1}{81}.
\left(1-9x^{2}\right)\left(1+9x^{2}\right)
Consider 1-81x^{4}. Rewrite 1-81x^{4} as 1^{2}-\left(9x^{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
\left(-9x^{2}+1\right)\left(9x^{2}+1\right)
Reorder the terms.
\left(1-3x\right)\left(1+3x\right)
Consider -9x^{2}+1. Rewrite -9x^{2}+1 as 1^{2}-\left(3x\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
\left(-3x+1\right)\left(3x+1\right)
Reorder the terms.
\frac{\left(-3x+1\right)\left(3x+1\right)\left(9x^{2}+1\right)}{81}
Rewrite the complete factored expression. Polynomial 9x^{2}+1 is not factored since it does not have any rational roots.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}