Question

Please answer this question with steps

Answer 1

Answer:

Step-by-step explanation:

$\sf \dfrac{1}{3}a^3-\dfrac{3}{4}a^2-\dfrac{5}{2}-\left[\dfrac{5}{2}a^2+\dfrac{3}{2}a^3+\dfrac{a}{3}-\dfrac{6}{5}\right]=$

               $\sf = \dfrac{1}{3}a^3-\dfrac{3}{4}a^2-\dfrac{5}{2}-\dfrac{5}{2}a^2-\dfrac{3}{2}a^3-\dfrac{a}{3}+\dfrac{6}{5}\\\\\\( Combine \ like \ terms)\\\\= \dfrac{1}{3}a^3 -\dfrac{3}{2}a^3 -\dfrac{3}{4}a^2-\dfrac{5}{2}a^2-\dfrac{a}{3}-\dfrac{5}{2}+\dfrac{6}{5}\\\\=\left[\dfrac{1*2}{3*2}-\dfrac{3*3}{2*3}\right]a^3 + \left[-\dfrac{3}{4}-\dfrac{5*2}{2*2}\right]a^2-\dfrac{a}{3}+\left[-\dfrac{5*5}{2*5}+\dfrac{6*2}{5*2}\right]$

               $\sf ==\left[\dfrac{2}{6}-\dfrac{9}{6}\right]a^3+\left[-\dfrac{3}{4}-\dfrac{10}{4}\right]a^2-\dfrac{a}{3}+\left[-\dfrac{25}{10}+\dfrac{12}{10}\right]\\\\=\dfrac{2-9}{6}a^3+\dfrac{(-3-10)}{4}a^2-\dfrac{a}{3}+\dfrac{(-25+12)}{15}$

               $\sf = \dfrac{-7}{6}a^3+ \dfrac{(-13)}{4}a^2-\dfrac{a}{3}+\dfrac{(-13)}{15}\\\\=-\dfrac{7}{6}a^3-\dfrac{13}{4}a^2-\dfrac{a}{3}-\dfrac{13}{15}$

Answer 2

Answer:

see explanation

Step-by-step explanation:

$\frac{1}{3}$ a³ - $\frac{3}{4}$ a² - $\frac{5}{2}$ - ( $\frac{5}{2}$ a² + $\frac{3}{2}$ a³ + $\frac{a}{3}$ - $\frac{6}{5}$ ) ← distribute parenthesis by - 1

= $\frac{1}{3}$ a³ - $\frac{3}{4}$ a² - $\frac{5}{2}$ - $\frac{5}{2}$ a² - $\frac{3}{2}$ a³ - $\frac{a}{3}$ + $\frac{6}{5}$ ← collect like terms

= ($\frac{1}{3}$ a³ - $\frac{3}{2}$ a³ ) + (-$\frac{3}{4}$ a² - $\frac{5}{2}$ a² ) - $\frac{a}{3}$ + (- $\frac{5}{2}$ + $\frac{6}{5}$ ) ← change to common denominators

=   ($\frac{2}{6}$ a³ - $\frac{9}{6}$ a³ ) + (- $\frac{3}{4}$ a² - $\frac{10}{4}$ a² ) - $\frac{a}{3}$ + (- $\frac{25}{10}$ + $\frac{12}{10}$ ) ← simplify

= - $\frac{7}{6}$ a³ - $\frac{13}{4}$ a² - $\frac{1}{3}$ a - $\frac{13}{10}$