Evaluate
8\left(m-2n\right)^{2}
Expand
8m^{2}-32mn+32n^{2}
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4m^{2}-16mn+16n^{2}+\left(2m-4n\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2m-4n\right)^{2}.
4m^{2}-16mn+16n^{2}+4m^{2}-16mn+16n^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2m-4n\right)^{2}.
8m^{2}-16mn+16n^{2}-16mn+16n^{2}
Combine 4m^{2} and 4m^{2} to get 8m^{2}.
8m^{2}-32mn+16n^{2}+16n^{2}
Combine -16mn and -16mn to get -32mn.
8m^{2}-32mn+32n^{2}
Combine 16n^{2} and 16n^{2} to get 32n^{2}.
4m^{2}-16mn+16n^{2}+\left(2m-4n\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2m-4n\right)^{2}.
4m^{2}-16mn+16n^{2}+4m^{2}-16mn+16n^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2m-4n\right)^{2}.
8m^{2}-16mn+16n^{2}-16mn+16n^{2}
Combine 4m^{2} and 4m^{2} to get 8m^{2}.
8m^{2}-32mn+16n^{2}+16n^{2}
Combine -16mn and -16mn to get -32mn.
8m^{2}-32mn+32n^{2}
Combine 16n^{2} and 16n^{2} to get 32n^{2}.
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