Expand
x^{2}+10x+y^{2}-8y+25
Evaluate
\left(x+5\right)^{2}+\left(y-4\right)^{2}-16
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x^{2}+10x+25+\left(y-4\right)^{2}-16
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.
x^{2}+10x+25+y^{2}-8y+16-16
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-4\right)^{2}.
x^{2}+10x+41+y^{2}-8y-16
Add 25 and 16 to get 41.
x^{2}+10x+25+y^{2}-8y
Subtract 16 from 41 to get 25.
x^{2}+10x+25+\left(y-4\right)^{2}-16
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.
x^{2}+10x+25+y^{2}-8y+16-16
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-4\right)^{2}.
x^{2}+10x+41+y^{2}-8y-16
Add 25 and 16 to get 41.
x^{2}+10x+25+y^{2}-8y
Subtract 16 from 41 to get 25.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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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}