Evaluate
-2x\left(y+a\right)+\left(x+y\right)^{2}-2y
Expand
x^{2}-2ax+y^{2}-2y
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x^{2}+2xy+y^{2}-2y-2x\left(a+y\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+y\right)^{2}.
x^{2}+2xy+y^{2}-2y-2xa-2xy
Use the distributive property to multiply -2x by a+y.
x^{2}+y^{2}-2y-2xa
Combine 2xy and -2xy to get 0.
x^{2}+2xy+y^{2}-2y-2x\left(a+y\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+y\right)^{2}.
x^{2}+2xy+y^{2}-2y-2xa-2xy
Use the distributive property to multiply -2x by a+y.
x^{2}+y^{2}-2y-2xa
Combine 2xy and -2xy to get 0.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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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}