Expand
x^{2}-14x+y^{2}-6y-7
Evaluate
\left(x-7\right)^{2}+\left(y-3\right)^{2}-65
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x^{2}-14x+49+\left(y-3\right)^{2}-65
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-7\right)^{2}.
x^{2}-14x+49+y^{2}-6y+9-65
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-3\right)^{2}.
x^{2}-14x+58+y^{2}-6y-65
Add 49 and 9 to get 58.
x^{2}-14x-7+y^{2}-6y
Subtract 65 from 58 to get -7.
x^{2}-14x+49+\left(y-3\right)^{2}-65
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-7\right)^{2}.
x^{2}-14x+49+y^{2}-6y+9-65
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-3\right)^{2}.
x^{2}-14x+58+y^{2}-6y-65
Add 49 and 9 to get 58.
x^{2}-14x-7+y^{2}-6y
Subtract 65 from 58 to get -7.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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
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