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\frac{1}{4}b^{2}+b+1
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(\frac{1}{2}b+1\right)^{2}.
\frac{1}{4}b^{2}+b+1
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(\frac{1}{2}b+1\right)^{2}.