Evaluate
\frac{2x\left(x-9y\right)}{3}
Expand
-6xy+\frac{2x^{2}}{3}
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\frac{2}{3}x^{2}-2xy-\frac{\frac{\frac{2}{3}x^{3}}{\frac{x}{2y}}}{\frac{x}{3}}
Use the distributive property to multiply \frac{2}{3}x by x-3y.
\frac{2}{3}x^{2}-2xy-\frac{\frac{2}{3}x^{3}\times 3}{\frac{x}{2y}x}
Divide \frac{\frac{2}{3}x^{3}}{\frac{x}{2y}} by \frac{x}{3} by multiplying \frac{\frac{2}{3}x^{3}}{\frac{x}{2y}} by the reciprocal of \frac{x}{3}.
\frac{2}{3}x^{2}-2xy-\frac{2x^{3}}{\frac{x}{2y}x}
Multiply \frac{2}{3} and 3 to get 2.
\frac{2}{3}x^{2}-2xy-\frac{2x^{3}}{\frac{xx}{2y}}
Express \frac{x}{2y}x as a single fraction.
\frac{2}{3}x^{2}-2xy-\frac{2x^{3}\times 2y}{xx}
Divide 2x^{3} by \frac{xx}{2y} by multiplying 2x^{3} by the reciprocal of \frac{xx}{2y}.
\frac{2}{3}x^{2}-2xy-2\times 2xy
Cancel out xx in both numerator and denominator.
\frac{2}{3}x^{2}-2xy-4xy
Multiply 2 and 2 to get 4.
\frac{2}{3}x^{2}-6xy
Combine -2xy and -4xy to get -6xy.
\frac{2}{3}x^{2}-2xy-\frac{\frac{\frac{2}{3}x^{3}}{\frac{x}{2y}}}{\frac{x}{3}}
Use the distributive property to multiply \frac{2}{3}x by x-3y.
\frac{2}{3}x^{2}-2xy-\frac{\frac{2}{3}x^{3}\times 3}{\frac{x}{2y}x}
Divide \frac{\frac{2}{3}x^{3}}{\frac{x}{2y}} by \frac{x}{3} by multiplying \frac{\frac{2}{3}x^{3}}{\frac{x}{2y}} by the reciprocal of \frac{x}{3}.
\frac{2}{3}x^{2}-2xy-\frac{2x^{3}}{\frac{x}{2y}x}
Multiply \frac{2}{3} and 3 to get 2.
\frac{2}{3}x^{2}-2xy-\frac{2x^{3}}{\frac{xx}{2y}}
Express \frac{x}{2y}x as a single fraction.
\frac{2}{3}x^{2}-2xy-\frac{2x^{3}\times 2y}{xx}
Divide 2x^{3} by \frac{xx}{2y} by multiplying 2x^{3} by the reciprocal of \frac{xx}{2y}.
\frac{2}{3}x^{2}-2xy-2\times 2xy
Cancel out xx in both numerator and denominator.
\frac{2}{3}x^{2}-2xy-4xy
Multiply 2 and 2 to get 4.
\frac{2}{3}x^{2}-6xy
Combine -2xy and -4xy to get -6xy.
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}