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-6y
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\frac{2}{3}\times 6x+\frac{2}{3}\times 3y-\frac{4}{5}\left(5x+10y\right)
Use the distributive property to multiply \frac{2}{3} by 6x+3y.
\frac{2\times 6}{3}x+\frac{2}{3}\times 3y-\frac{4}{5}\left(5x+10y\right)
Express \frac{2}{3}\times 6 as a single fraction.
\frac{12}{3}x+\frac{2}{3}\times 3y-\frac{4}{5}\left(5x+10y\right)
Multiply 2 and 6 to get 12.
4x+\frac{2}{3}\times 3y-\frac{4}{5}\left(5x+10y\right)
Divide 12 by 3 to get 4.
4x+2y-\frac{4}{5}\left(5x+10y\right)
Cancel out 3 and 3.
4x+2y-\frac{4}{5}\times 5x-\frac{4}{5}\times 10y
Use the distributive property to multiply -\frac{4}{5} by 5x+10y.
4x+2y-4x-\frac{4}{5}\times 10y
Cancel out 5 and 5.
4x+2y-4x+\frac{-4\times 10}{5}y
Express -\frac{4}{5}\times 10 as a single fraction.
4x+2y-4x+\frac{-40}{5}y
Multiply -4 and 10 to get -40.
4x+2y-4x-8y
Divide -40 by 5 to get -8.
2y-8y
Combine 4x and -4x to get 0.
-6y
Combine 2y and -8y to get -6y.
\frac{2}{3}\times 6x+\frac{2}{3}\times 3y-\frac{4}{5}\left(5x+10y\right)
Use the distributive property to multiply \frac{2}{3} by 6x+3y.
\frac{2\times 6}{3}x+\frac{2}{3}\times 3y-\frac{4}{5}\left(5x+10y\right)
Express \frac{2}{3}\times 6 as a single fraction.
\frac{12}{3}x+\frac{2}{3}\times 3y-\frac{4}{5}\left(5x+10y\right)
Multiply 2 and 6 to get 12.
4x+\frac{2}{3}\times 3y-\frac{4}{5}\left(5x+10y\right)
Divide 12 by 3 to get 4.
4x+2y-\frac{4}{5}\left(5x+10y\right)
Cancel out 3 and 3.
4x+2y-\frac{4}{5}\times 5x-\frac{4}{5}\times 10y
Use the distributive property to multiply -\frac{4}{5} by 5x+10y.
4x+2y-4x-\frac{4}{5}\times 10y
Cancel out 5 and 5.
4x+2y-4x+\frac{-4\times 10}{5}y
Express -\frac{4}{5}\times 10 as a single fraction.
4x+2y-4x+\frac{-40}{5}y
Multiply -4 and 10 to get -40.
4x+2y-4x-8y
Divide -40 by 5 to get -8.
2y-8y
Combine 4x and -4x to get 0.
-6y
Combine 2y and -8y to get -6y.
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}