Evaluate
\left(x-y+3\right)\left(1+y-x\right)
Expand
3+2y-y^{2}-2x+2xy-x^{2}
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\left(-x\right)x-\left(-x\right)y+3\left(-x\right)+yx-y^{2}+3y+x-y+3
Apply the distributive property by multiplying each term of -x+y+1 by each term of x-y+3.
\left(-x\right)x+xy+3\left(-x\right)+yx-y^{2}+3y+x-y+3
Multiply -1 and -1 to get 1.
\left(-x\right)x+2xy+3\left(-x\right)-y^{2}+3y+x-y+3
Combine xy and yx to get 2xy.
\left(-x\right)x+2xy+3\left(-x\right)-y^{2}+2y+x+3
Combine 3y and -y to get 2y.
-x^{2}+2xy+3\left(-1\right)x-y^{2}+2y+x+3
Multiply x and x to get x^{2}.
-x^{2}+2xy-3x-y^{2}+2y+x+3
Multiply 3 and -1 to get -3.
-x^{2}+2xy-2x-y^{2}+2y+3
Combine -3x and x to get -2x.
\left(-x\right)x-\left(-x\right)y+3\left(-x\right)+yx-y^{2}+3y+x-y+3
Apply the distributive property by multiplying each term of -x+y+1 by each term of x-y+3.
\left(-x\right)x+xy+3\left(-x\right)+yx-y^{2}+3y+x-y+3
Multiply -1 and -1 to get 1.
\left(-x\right)x+2xy+3\left(-x\right)-y^{2}+3y+x-y+3
Combine xy and yx to get 2xy.
\left(-x\right)x+2xy+3\left(-x\right)-y^{2}+2y+x+3
Combine 3y and -y to get 2y.
-x^{2}+2xy+3\left(-1\right)x-y^{2}+2y+x+3
Multiply x and x to get x^{2}.
-x^{2}+2xy-3x-y^{2}+2y+x+3
Multiply 3 and -1 to get -3.
-x^{2}+2xy-2x-y^{2}+2y+3
Combine -3x and x to get -2x.
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}