Evaluate
x^{2}+2\sqrt{82}x-18
Expand
x^{2}+2\sqrt{82}x-18
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\left(\sqrt{82}\right)^{2}+2\sqrt{82}x+x^{2}-100
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{82}+x\right)^{2}.
82+2\sqrt{82}x+x^{2}-100
The square of \sqrt{82} is 82.
-18+2\sqrt{82}x+x^{2}
Subtract 100 from 82 to get -18.
\left(\sqrt{82}\right)^{2}+2\sqrt{82}x+x^{2}-100
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{82}+x\right)^{2}.
82+2\sqrt{82}x+x^{2}-100
The square of \sqrt{82} is 82.
-18+2\sqrt{82}x+x^{2}
Subtract 100 from 82 to get -18.
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