Evaluate
\frac{x^{4}}{2}+\frac{2x^{3}}{3}+1
Expand
\frac{x^{4}}{2}+\frac{2x^{3}}{3}+1
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\left(x+\frac{4}{3}\right)\times \frac{1}{2}x^{3}+1
Divide 2x^{3} by 4 to get \frac{1}{2}x^{3}.
\left(\frac{1}{2}x+\frac{2}{3}\right)x^{3}+1
Use the distributive property to multiply x+\frac{4}{3} by \frac{1}{2}.
\frac{1}{2}x^{4}+\frac{2}{3}x^{3}+1
Use the distributive property to multiply \frac{1}{2}x+\frac{2}{3} by x^{3}.
\left(x+\frac{4}{3}\right)\times \frac{1}{2}x^{3}+1
Divide 2x^{3} by 4 to get \frac{1}{2}x^{3}.
\left(\frac{1}{2}x+\frac{2}{3}\right)x^{3}+1
Use the distributive property to multiply x+\frac{4}{3} by \frac{1}{2}.
\frac{1}{2}x^{4}+\frac{2}{3}x^{3}+1
Use the distributive property to multiply \frac{1}{2}x+\frac{2}{3} by x^{3}.
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