Evaluate
\frac{9x^{3}}{2}-\frac{47xy}{12}+\frac{8y^{2}}{3}-\frac{13x^{2}}{4}+\frac{3y}{4}+\frac{5x}{3}
Expand
\frac{9x^{3}}{2}-\frac{47xy}{12}+\frac{8y^{2}}{3}-\frac{13x^{2}}{4}+\frac{3y}{4}+\frac{5x}{3}
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\frac{5}{3}x+\frac{3}{4}y-\frac{9}{2}x^{2}\left(1-x\right)-\left(-\frac{5}{4}x+\frac{8}{3}y\right)\left(x-y\right)
Multiply 5 and \frac{1}{3} to get \frac{5}{3}.
\frac{5}{3}x+\frac{3}{4}y-\frac{9}{2}x^{2}\left(1-x\right)-\left(-\frac{5}{4}x^{2}+\frac{47}{12}xy-\frac{8}{3}y^{2}\right)
Use the distributive property to multiply -\frac{5}{4}x+\frac{8}{3}y by x-y and combine like terms.
\frac{5}{3}x+\frac{3}{4}y-\frac{9}{2}x^{2}\left(1-x\right)+\frac{5}{4}x^{2}-\frac{47}{12}xy+\frac{8}{3}y^{2}
To find the opposite of -\frac{5}{4}x^{2}+\frac{47}{12}xy-\frac{8}{3}y^{2}, find the opposite of each term.
\frac{5}{3}x+\frac{3}{4}y-\frac{9}{2}x^{2}+\frac{9}{2}x^{3}+\frac{5}{4}x^{2}-\frac{47}{12}xy+\frac{8}{3}y^{2}
Use the distributive property to multiply -\frac{9}{2}x^{2} by 1-x.
\frac{5}{3}x+\frac{3}{4}y-\frac{13}{4}x^{2}+\frac{9}{2}x^{3}-\frac{47}{12}xy+\frac{8}{3}y^{2}
Combine -\frac{9}{2}x^{2} and \frac{5}{4}x^{2} to get -\frac{13}{4}x^{2}.
\frac{5}{3}x+\frac{3}{4}y-\frac{9}{2}x^{2}\left(1-x\right)-\left(-\frac{5}{4}x+\frac{8}{3}y\right)\left(x-y\right)
Multiply 5 and \frac{1}{3} to get \frac{5}{3}.
\frac{5}{3}x+\frac{3}{4}y-\frac{9}{2}x^{2}\left(1-x\right)-\left(-\frac{5}{4}x^{2}+\frac{47}{12}xy-\frac{8}{3}y^{2}\right)
Use the distributive property to multiply -\frac{5}{4}x+\frac{8}{3}y by x-y and combine like terms.
\frac{5}{3}x+\frac{3}{4}y-\frac{9}{2}x^{2}\left(1-x\right)+\frac{5}{4}x^{2}-\frac{47}{12}xy+\frac{8}{3}y^{2}
To find the opposite of -\frac{5}{4}x^{2}+\frac{47}{12}xy-\frac{8}{3}y^{2}, find the opposite of each term.
\frac{5}{3}x+\frac{3}{4}y-\frac{9}{2}x^{2}+\frac{9}{2}x^{3}+\frac{5}{4}x^{2}-\frac{47}{12}xy+\frac{8}{3}y^{2}
Use the distributive property to multiply -\frac{9}{2}x^{2} by 1-x.
\frac{5}{3}x+\frac{3}{4}y-\frac{13}{4}x^{2}+\frac{9}{2}x^{3}-\frac{47}{12}xy+\frac{8}{3}y^{2}
Combine -\frac{9}{2}x^{2} and \frac{5}{4}x^{2} to get -\frac{13}{4}x^{2}.
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