Evaluate
3xy+\frac{4x^{2}}{9}
Expand
3xy+\frac{4x^{2}}{9}
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\frac{4}{9}x^{2}+3xy+\frac{81}{16}y^{2}-\left(-\frac{9}{4}y\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\frac{2}{3}x+\frac{9}{4}y\right)^{2}.
\frac{4}{9}x^{2}+3xy+\frac{81}{16}y^{2}-\left(-\frac{9}{4}\right)^{2}y^{2}
Expand \left(-\frac{9}{4}y\right)^{2}.
\frac{4}{9}x^{2}+3xy+\frac{81}{16}y^{2}-\frac{81}{16}y^{2}
Calculate -\frac{9}{4} to the power of 2 and get \frac{81}{16}.
\frac{4}{9}x^{2}+3xy
Combine \frac{81}{16}y^{2} and -\frac{81}{16}y^{2} to get 0.
\frac{4}{9}x^{2}+3xy+\frac{81}{16}y^{2}-\left(-\frac{9}{4}y\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\frac{2}{3}x+\frac{9}{4}y\right)^{2}.
\frac{4}{9}x^{2}+3xy+\frac{81}{16}y^{2}-\left(-\frac{9}{4}\right)^{2}y^{2}
Expand \left(-\frac{9}{4}y\right)^{2}.
\frac{4}{9}x^{2}+3xy+\frac{81}{16}y^{2}-\frac{81}{16}y^{2}
Calculate -\frac{9}{4} to the power of 2 and get \frac{81}{16}.
\frac{4}{9}x^{2}+3xy
Combine \frac{81}{16}y^{2} and -\frac{81}{16}y^{2} to get 0.
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