Evaluate
\frac{3\left(2x-1\right)\left(x^{3}+8\right)}{x}
Expand
6x^{3}-3x^{2}+48-\frac{24}{x}
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3\left(-x^{3}\right)x^{-1}-6\left(-x^{3}\right)-24x^{-1}+48
Use the distributive property to multiply -x^{3}-8 by 3x^{-1}-6.
3\left(-x^{3}\right)x^{-1}+6x^{3}-24x^{-1}+48
Multiply -6 and -1 to get 6.
-3x^{3}x^{-1}+6x^{3}-24x^{-1}+48
Multiply 3 and -1 to get -3.
-3x^{2}+6x^{3}-24x^{-1}+48
To multiply powers of the same base, add their exponents. Add 3 and -1 to get 2.
3\left(-x^{3}\right)x^{-1}-6\left(-x^{3}\right)-24x^{-1}+48
Use the distributive property to multiply -x^{3}-8 by 3x^{-1}-6.
3\left(-x^{3}\right)x^{-1}+6x^{3}-24x^{-1}+48
Multiply -6 and -1 to get 6.
-3x^{3}x^{-1}+6x^{3}-24x^{-1}+48
Multiply 3 and -1 to get -3.
-3x^{2}+6x^{3}-24x^{-1}+48
To multiply powers of the same base, add their exponents. Add 3 and -1 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}