Evaluate
\left(x-y-2\right)\left(x+y-6\right)
Expand
x^{2}-8x-y^{2}+4y+12
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x^{2}-8x+16-\left(y-2\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.
x^{2}-8x+16-\left(y^{2}-4y+4\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-2\right)^{2}.
x^{2}-8x+16-y^{2}+4y-4
To find the opposite of y^{2}-4y+4, find the opposite of each term.
x^{2}-8x+12-y^{2}+4y
Subtract 4 from 16 to get 12.
x^{2}-8x+16-\left(y-2\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.
x^{2}-8x+16-\left(y^{2}-4y+4\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-2\right)^{2}.
x^{2}-8x+16-y^{2}+4y-4
To find the opposite of y^{2}-4y+4, find the opposite of each term.
x^{2}-8x+12-y^{2}+4y
Subtract 4 from 16 to get 12.
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
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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}