question_answer

Take away\[\left( \frac{8}{5}{{x}^{2}}-\frac{2}{3}{{x}^{3}}+\frac{3}{2}x-1 \right)\] from \[\left( \frac{{{x}^{3}}}{5}-\frac{3}{2}{{x}^{2}}+\frac{2}{3}x+1 \right)\]

Answer:

We have \[\left( \frac{{{x}^{3}}}{5}-\frac{3}{2}{{x}^{2}}+\frac{2}{3}x+\frac{1}{4} \right)-\left( \frac{8}{5}{{x}^{2}}-\frac{2}{3}{{x}^{3}}+\frac{3}{2}x-1 \right)\] \[=\frac{{{x}^{3}}}{5}-\frac{3}{2}{{x}^{2}}+\frac{2}{3}x+\frac{1}{4}-\left(\frac{8}{5}{{x}^{2}}-\frac{2}{3}{{x}^{3}}+\frac{3}{2}x-1 \right)\] \[=\left( \frac{1}{5}+\frac{2}{3} \right){{x}^{3}}+\left( -\frac{3}{2}-\frac{8}{5} \right){{x}^{2}}+\left( \frac{2}{3}-\frac{3}{2} \right)x+\left( \frac{1}{4}-1 \right)\]\[=\frac{13{{x}^{3}}}{15}-\frac{31{{x}^{2}}}{10}-\frac{5x}{6}+\frac{5}{4}\]