Evaluate
\left(a+4d\right)^{2}+a^{2}
Expand
2a^{2}+8ad+16d^{2}
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a^{2}+a^{2}+8ad+16d^{2}
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+4d\right)^{2}.
2a^{2}+8ad+16d^{2}
Combine a^{2} and a^{2} to get 2a^{2}.
a^{2}+a^{2}+8ad+16d^{2}
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+4d\right)^{2}.
2a^{2}+8ad+16d^{2}
Combine a^{2} and a^{2} to get 2a^{2}.
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