Answer:
see explanation
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] a³ - [tex]\frac{3}{4}[/tex] a² - [tex]\frac{5}{2}[/tex] - ( [tex]\frac{5}{2}[/tex] a² + [tex]\frac{3}{2}[/tex] a³ + [tex]\frac{a}{3}[/tex] - [tex]\frac{6}{5}[/tex] ) ← distribute parenthesis by - 1
= [tex]\frac{1}{3}[/tex] a³ - [tex]\frac{3}{4}[/tex] a² - [tex]\frac{5}{2}[/tex] - [tex]\frac{5}{2}[/tex] a² - [tex]\frac{3}{2}[/tex] a³ - [tex]\frac{a}{3}[/tex] + [tex]\frac{6}{5}[/tex] ← collect like terms
= ([tex]\frac{1}{3}[/tex] a³ - [tex]\frac{3}{2}[/tex] a³ ) + (-[tex]\frac{3}{4}[/tex] a² - [tex]\frac{5}{2}[/tex] a² ) - [tex]\frac{a}{3}[/tex] + (- [tex]\frac{5}{2}[/tex] + [tex]\frac{6}{5}[/tex] ) ← change to common denominators
= ([tex]\frac{2}{6}[/tex] a³ - [tex]\frac{9}{6}[/tex] a³ ) + (- [tex]\frac{3}{4}[/tex] a² - [tex]\frac{10}{4}[/tex] a² ) - [tex]\frac{a}{3}[/tex] + (- [tex]\frac{25}{10}[/tex] + [tex]\frac{12}{10}[/tex] ) ← simplify
= - [tex]\frac{7}{6}[/tex] a³ - [tex]\frac{13}{4}[/tex] a² - [tex]\frac{1}{3}[/tex] a - [tex]\frac{13}{10}[/tex]
Answer:
Step-by-step explanation:
[tex]\sf \dfrac{1}{3}a^3-\dfrac{3}{4}a^2-\dfrac{5}{2}-\left[\dfrac{5}{2}a^2+\dfrac{3}{2}a^3+\dfrac{a}{3}-\dfrac{6}{5}\right]=[/tex]
[tex]\sf = \dfrac{1}{3}a^3-\dfrac{3}{4}a^2-\dfrac{5}{2}-\dfrac{5}{2}a^2-\dfrac{3}{2}a^3-\dfrac{a}{3}+\dfrac{6}{5}\\\\\\( Combine \ like \ terms)\\\\= \dfrac{1}{3}a^3 -\dfrac{3}{2}a^3 -\dfrac{3}{4}a^2-\dfrac{5}{2}a^2-\dfrac{a}{3}-\dfrac{5}{2}+\dfrac{6}{5}\\\\=\left[\dfrac{1*2}{3*2}-\dfrac{3*3}{2*3}\right]a^3 + \left[-\dfrac{3}{4}-\dfrac{5*2}{2*2}\right]a^2-\dfrac{a}{3}+\left[-\dfrac{5*5}{2*5}+\dfrac{6*2}{5*2}\right]\\\\\\[/tex]
[tex]\sf ==\left[\dfrac{2}{6}-\dfrac{9}{6}\right]a^3+\left[-\dfrac{3}{4}-\dfrac{10}{4}\right]a^2-\dfrac{a}{3}+\left[-\dfrac{25}{10}+\dfrac{12}{10}\right]\\\\=\dfrac{2-9}{6}a^3+\dfrac{(-3-10)}{4}a^2-\dfrac{a}{3}+\dfrac{(-25+12)}{15}\\\\[/tex]
[tex]\sf = \dfrac{-7}{6}a^3+ \dfrac{(-13)}{4}a^2-\dfrac{a}{3}+\dfrac{(-13)}{15}\\\\=-\dfrac{7}{6}a^3-\dfrac{13}{4}a^2-\dfrac{a}{3}-\dfrac{13}{15}[/tex]