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