Evaluate
5\left(a^{2}+b^{2}\right)
Expand
5a^{2}+5b^{2}
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a^{2}+4ab+4b^{2}+\left(2a-b\right)^{2}
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+2b\right)^{2}.
a^{2}+4ab+4b^{2}+4a^{2}-4ab+b^{2}
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(2a-b\right)^{2}.
5a^{2}+4ab+4b^{2}-4ab+b^{2}
Combine a^{2} and 4a^{2} to get 5a^{2}.
5a^{2}+4b^{2}+b^{2}
Combine 4ab and -4ab to get 0.
5a^{2}+5b^{2}
Combine 4b^{2} and b^{2} to get 5b^{2}.
a^{2}+4ab+4b^{2}+\left(2a-b\right)^{2}
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+2b\right)^{2}.
a^{2}+4ab+4b^{2}+4a^{2}-4ab+b^{2}
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(2a-b\right)^{2}.
5a^{2}+4ab+4b^{2}-4ab+b^{2}
Combine a^{2} and 4a^{2} to get 5a^{2}.
5a^{2}+4b^{2}+b^{2}
Combine 4ab and -4ab to get 0.
5a^{2}+5b^{2}
Combine 4b^{2} and b^{2} to get 5b^{2}.
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