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\frac{4}{9}y^{2}-\frac{8}{3}y+4
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\frac{2}{3}y-2\right)^{2}.
\frac{4}{9}y^{2}-\frac{8}{3}y+4
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\frac{2}{3}y-2\right)^{2}.