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\frac{1}{16}x^{2}+\frac{1}{3}xy+\frac{4}{9}y^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\frac{1}{4}x+\frac{2}{3}y\right)^{2}.
\frac{1}{16}x^{2}+\frac{1}{3}xy+\frac{4}{9}y^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\frac{1}{4}x+\frac{2}{3}y\right)^{2}.