Question

Addition of $\frac{a^2}{2}+\frac{b^3}{3}+\frac{c^3}{4},\frac{2a^2}{3}+\frac{3b^3}{4}-\frac{4c^3}{5}$ and $a^2+b^3+c^3$ is

Answer 1

$(\frac{a^2}{2}+\frac{b^3}{3}+\frac{c^3}{4})+(\frac{2a^2}{3}+\frac{3b^3}{4}-\frac{4c^3}{5})+(a^2+b^3+c^3)$

$\Rightarrow$ Collecting respective coefficient of $a^2,b^3,c^3$ in one bracket.

$a^2(\frac{1}{2}+\frac{2}{3}+1)+b^3(\frac{1}{3}+\frac{3}{4}+1)+c^3(\frac{1}{4}-\frac{4}{5}+1)$

$=a^2\left(\frac{3+4+6}{6}\right)+b^3\left(\frac{4+9+12}{12}\right)+c^3\left(\frac{5-16+20}{20}\right)$

$=a^2\left(\frac{13}{6}\right)+b^3\left(\frac{25}{12}\right)+c^3\left(\frac{9}{20}\right)$

$=\frac{13}{6}{a}^2+\frac{25}{12}{b}^3+\frac{9}{20}{c}^3$