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\frac{1}{36}x^{2}+\frac{2}{9}x+\frac{4}{9}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\frac{1}{6}x+\frac{2}{3}\right)^{2}.
\frac{1}{36}x^{2}+\frac{2}{9}x+\frac{4}{9}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\frac{1}{6}x+\frac{2}{3}\right)^{2}.