Evaluate
\left(y+6\right)^{2}+\left(x-6\right)^{2}
Expand
x^{2}-12x+y^{2}+12y+72
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x^{2}-12x+36+\left(y+6\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.
x^{2}-12x+36+y^{2}+12y+36
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(y+6\right)^{2}.
x^{2}-12x+72+y^{2}+12y
Add 36 and 36 to get 72.
x^{2}-12x+36+\left(y+6\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.
x^{2}-12x+36+y^{2}+12y+36
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(y+6\right)^{2}.
x^{2}-12x+72+y^{2}+12y
Add 36 and 36 to get 72.
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