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\frac{4}{9}x^{2}+\frac{4}{15}xy+\frac{1}{25}y^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\frac{2}{3}x+\frac{1}{5}y\right)^{2}.
\frac{4}{9}x^{2}+\frac{4}{15}xy+\frac{1}{25}y^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\frac{2}{3}x+\frac{1}{5}y\right)^{2}.