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9a^{2}+3ab+\frac{1}{4}b^{2}
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(3a+\frac{1}{2}b\right)^{2}.
9a^{2}+3ab+\frac{1}{4}b^{2}
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(3a+\frac{1}{2}b\right)^{2}.