( 3 ) 2 a \sqrt { 3 a b ^ { 2 } } - ( \frac { b } { 6 } \sqrt { 27 a ^ { 3 } } - 2 a b \sqrt { \frac { 3 } { 4 } a ) }
Factor
\frac{\sqrt{3}\left(12|b|+b\right)a^{\frac{3}{2}}}{2}
Evaluate
\frac{\sqrt{3}\left(12|b|+b\right)a^{\frac{3}{2}}}{2}
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\frac{36a\sqrt{3}\sqrt{ab^{2}}-\left(b\times 3\sqrt{3}a^{\frac{3}{2}}-12ab\times \frac{2\sqrt{3}\sqrt{a}}{4}\right)}{6}
Factor out \frac{1}{6}.
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}