Evaluate
\left(x+y-z-2\right)\left(-x+y+z-2\right)
Expand
4-z^{2}-4y+y^{2}+2xz-x^{2}
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\left(-x\right)x+\left(-x\right)y-\left(-x\right)z-2\left(-x\right)+yx+y^{2}-yz-2y+zx+zy-z^{2}-2z-2x-2y+2z+4
Apply the distributive property by multiplying each term of -x+y+z-2 by each term of x+y-z-2.
\left(-x\right)x+\left(-x\right)y+xz-2\left(-x\right)+yx+y^{2}-yz-2y+zx+zy-z^{2}-2z-2x-2y+2z+4
Multiply -1 and -1 to get 1.
\left(-x\right)x+\left(-x\right)y+xz+2x+yx+y^{2}-yz-2y+zx+zy-z^{2}-2z-2x-2y+2z+4
Multiply -2 and -1 to get 2.
\left(-x\right)x+\left(-x\right)y+2xz+2x+yx+y^{2}-yz-2y+zy-z^{2}-2z-2x-2y+2z+4
Combine xz and zx to get 2xz.
\left(-x\right)x+\left(-x\right)y+2xz+2x+yx+y^{2}-2y-z^{2}-2z-2x-2y+2z+4
Combine -yz and zy to get 0.
\left(-x\right)x+\left(-x\right)y+2xz+yx+y^{2}-2y-z^{2}-2z-2y+2z+4
Combine 2x and -2x to get 0.
\left(-x\right)x+\left(-x\right)y+2xz+yx+y^{2}-4y-z^{2}-2z+2z+4
Combine -2y and -2y to get -4y.
\left(-x\right)x+\left(-x\right)y+2xz+yx+y^{2}-4y-z^{2}+4
Combine -2z and 2z to get 0.
-x^{2}-xy+2xz+yx+y^{2}-4y-z^{2}+4
Multiply x and x to get x^{2}.
-x^{2}+2xz+y^{2}-4y-z^{2}+4
Combine -xy and yx to get 0.
\left(-x\right)x+\left(-x\right)y-\left(-x\right)z-2\left(-x\right)+yx+y^{2}-yz-2y+zx+zy-z^{2}-2z-2x-2y+2z+4
Apply the distributive property by multiplying each term of -x+y+z-2 by each term of x+y-z-2.
\left(-x\right)x+\left(-x\right)y+xz-2\left(-x\right)+yx+y^{2}-yz-2y+zx+zy-z^{2}-2z-2x-2y+2z+4
Multiply -1 and -1 to get 1.
\left(-x\right)x+\left(-x\right)y+xz+2x+yx+y^{2}-yz-2y+zx+zy-z^{2}-2z-2x-2y+2z+4
Multiply -2 and -1 to get 2.
\left(-x\right)x+\left(-x\right)y+2xz+2x+yx+y^{2}-yz-2y+zy-z^{2}-2z-2x-2y+2z+4
Combine xz and zx to get 2xz.
\left(-x\right)x+\left(-x\right)y+2xz+2x+yx+y^{2}-2y-z^{2}-2z-2x-2y+2z+4
Combine -yz and zy to get 0.
\left(-x\right)x+\left(-x\right)y+2xz+yx+y^{2}-2y-z^{2}-2z-2y+2z+4
Combine 2x and -2x to get 0.
\left(-x\right)x+\left(-x\right)y+2xz+yx+y^{2}-4y-z^{2}-2z+2z+4
Combine -2y and -2y to get -4y.
\left(-x\right)x+\left(-x\right)y+2xz+yx+y^{2}-4y-z^{2}+4
Combine -2z and 2z to get 0.
-x^{2}-xy+2xz+yx+y^{2}-4y-z^{2}+4
Multiply x and x to get x^{2}.
-x^{2}+2xz+y^{2}-4y-z^{2}+4
Combine -xy and yx 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}