Evaluate
3xy+x-y^{2}
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3xy+x-y^{2}
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3x-\left(2yx+y^{2}\right)-\left(3x-y\right)\times 2x+y+\left(3x-1\right)\left(2x+y\right)
Use the distributive property to multiply y by 2x+y.
3x-2yx-y^{2}-\left(3x-y\right)\times 2x+y+\left(3x-1\right)\left(2x+y\right)
To find the opposite of 2yx+y^{2}, find the opposite of each term.
3x-2yx-y^{2}-\left(6x-2y\right)x+y+\left(3x-1\right)\left(2x+y\right)
Use the distributive property to multiply 3x-y by 2.
3x-2yx-y^{2}-\left(6x^{2}-2yx\right)+y+\left(3x-1\right)\left(2x+y\right)
Use the distributive property to multiply 6x-2y by x.
3x-2yx-y^{2}-6x^{2}-\left(-2yx\right)+y+\left(3x-1\right)\left(2x+y\right)
To find the opposite of 6x^{2}-2yx, find the opposite of each term.
3x-2yx-y^{2}-6x^{2}+2yx+y+\left(3x-1\right)\left(2x+y\right)
The opposite of -2yx is 2yx.
3x-y^{2}-6x^{2}+y+\left(3x-1\right)\left(2x+y\right)
Combine -2yx and 2yx to get 0.
3x-y^{2}-6x^{2}+y+6x^{2}+3xy-2x-y
Apply the distributive property by multiplying each term of 3x-1 by each term of 2x+y.
3x-y^{2}+y+3xy-2x-y
Combine -6x^{2} and 6x^{2} to get 0.
x-y^{2}+y+3xy-y
Combine 3x and -2x to get x.
x-y^{2}+3xy
Combine y and -y to get 0.
3x-\left(2yx+y^{2}\right)-\left(3x-y\right)\times 2x+y+\left(3x-1\right)\left(2x+y\right)
Use the distributive property to multiply y by 2x+y.
3x-2yx-y^{2}-\left(3x-y\right)\times 2x+y+\left(3x-1\right)\left(2x+y\right)
To find the opposite of 2yx+y^{2}, find the opposite of each term.
3x-2yx-y^{2}-\left(6x-2y\right)x+y+\left(3x-1\right)\left(2x+y\right)
Use the distributive property to multiply 3x-y by 2.
3x-2yx-y^{2}-\left(6x^{2}-2yx\right)+y+\left(3x-1\right)\left(2x+y\right)
Use the distributive property to multiply 6x-2y by x.
3x-2yx-y^{2}-6x^{2}-\left(-2yx\right)+y+\left(3x-1\right)\left(2x+y\right)
To find the opposite of 6x^{2}-2yx, find the opposite of each term.
3x-2yx-y^{2}-6x^{2}+2yx+y+\left(3x-1\right)\left(2x+y\right)
The opposite of -2yx is 2yx.
3x-y^{2}-6x^{2}+y+\left(3x-1\right)\left(2x+y\right)
Combine -2yx and 2yx to get 0.
3x-y^{2}-6x^{2}+y+6x^{2}+3xy-2x-y
Apply the distributive property by multiplying each term of 3x-1 by each term of 2x+y.
3x-y^{2}+y+3xy-2x-y
Combine -6x^{2} and 6x^{2} to get 0.
x-y^{2}+y+3xy-y
Combine 3x and -2x to get x.
x-y^{2}+3xy
Combine y and -y to get 0.
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}