Evaluate
a\left(a+2\right)+\left(a+1\right)^{2}
Expand
2a^{2}+4a+1
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a^{2}+2a+1+a\left(a+2\right)
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+1\right)^{2}.
a^{2}+2a+1+a^{2}+2a
Use the distributive property to multiply a by a+2.
2a^{2}+2a+1+2a
Combine a^{2} and a^{2} to get 2a^{2}.
2a^{2}+4a+1
Combine 2a and 2a to get 4a.
a^{2}+2a+1+a\left(a+2\right)
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+1\right)^{2}.
a^{2}+2a+1+a^{2}+2a
Use the distributive property to multiply a by a+2.
2a^{2}+2a+1+2a
Combine a^{2} and a^{2} to get 2a^{2}.
2a^{2}+4a+1
Combine 2a and 2a to get 4a.
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