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25x^{2}+\frac{2}{3}xy+\frac{1}{225}y^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5x+\frac{1}{15}y\right)^{2}.
25x^{2}+\frac{2}{3}xy+\frac{1}{225}y^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5x+\frac{1}{15}y\right)^{2}.