Evaluate
\frac{\left(a-1\right)\left(1-2a^{3}\right)}{a^{2}}
Expand
-2a^{2}+2a+\frac{1}{a}-\frac{1}{a^{2}}
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\left(a^{2}-a\right)\left(a^{-3}-2\right)
Use the distributive property to multiply a by a-1.
a^{2}a^{-3}-2a^{2}-aa^{-3}+2a
Use the distributive property to multiply a^{2}-a by a^{-3}-2.
a^{-1}-2a^{2}-aa^{-3}+2a
To multiply powers of the same base, add their exponents. Add 2 and -3 to get -1.
a^{-1}-2a^{2}-a^{-2}+2a
To multiply powers of the same base, add their exponents. Add 1 and -3 to get -2.
\left(a^{2}-a\right)\left(a^{-3}-2\right)
Use the distributive property to multiply a by a-1.
a^{2}a^{-3}-2a^{2}-aa^{-3}+2a
Use the distributive property to multiply a^{2}-a by a^{-3}-2.
a^{-1}-2a^{2}-aa^{-3}+2a
To multiply powers of the same base, add their exponents. Add 2 and -3 to get -1.
a^{-1}-2a^{2}-a^{-2}+2a
To multiply powers of the same base, add their exponents. Add 1 and -3 to get -2.
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}