Evaluate
2\left(4a^{2}+b^{2}\right)
Expand
8a^{2}+2b^{2}
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4a^{2}+4ab+b^{2}+\left(b-2a\right)^{2}
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(2a+b\right)^{2}.
4a^{2}+4ab+b^{2}+b^{2}-4ba+4a^{2}
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(b-2a\right)^{2}.
4a^{2}+4ab+2b^{2}-4ba+4a^{2}
Combine b^{2} and b^{2} to get 2b^{2}.
4a^{2}+2b^{2}+4a^{2}
Combine 4ab and -4ba to get 0.
8a^{2}+2b^{2}
Combine 4a^{2} and 4a^{2} to get 8a^{2}.
4a^{2}+4ab+b^{2}+\left(b-2a\right)^{2}
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(2a+b\right)^{2}.
4a^{2}+4ab+b^{2}+b^{2}-4ba+4a^{2}
Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(b-2a\right)^{2}.
4a^{2}+4ab+2b^{2}-4ba+4a^{2}
Combine b^{2} and b^{2} to get 2b^{2}.
4a^{2}+2b^{2}+4a^{2}
Combine 4ab and -4ba to get 0.
8a^{2}+2b^{2}
Combine 4a^{2} and 4a^{2} to get 8a^{2}.
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