Question

please solve this question anyone-

$\rm - \dfrac{1}{2} {a}^{2} {b}^{2}c + \dfrac{1}{3} a {b}^{2} c - \dfrac{1}{4}abc^{2} - \dfrac{1}{5} c {b}^{2} {a}^{2} + \dfrac{1}{6} c {b}^{2} {a} - \dfrac{}{7} {c}^{2}ab + \dfrac{1}{8} c {a}^{2} b$
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Answer 1

ANSWER:

To Solve:

$\:\:\bullet\:\:\rm -\dfrac{1}{2}a^2b^2c+\dfrac{1}{3}ab^2c-\dfrac{1}{4}abc^2-\dfrac{1}{5}cb^2a^2+\dfrac{1}{6}cb^2a-\dfrac{1}{7}c^2ab+\dfrac{1}{8}ca^2b$

Solution:

We are given that,

$\implies\rm -\dfrac{1}{2}a^2b^2c+\dfrac{1}{3}ab^2c-\dfrac{1}{4}abc^2-\dfrac{1}{5}cb^2a^2+\dfrac{1}{6}cb^2a-\dfrac{1}{7}c^2ab+\dfrac{1}{8}ca^2b$

Taking abc common,

$\implies\rm abc\left(-\dfrac{1}{2}ab+\dfrac{1}{3}b-\dfrac{1}{4}c-\dfrac{1}{5}ba+\dfrac{1}{6}b-\dfrac{1}{7}c+\dfrac{1}{8}a\right)$

Rearranging the terms,

$\implies\rm abc\left[\left(-\dfrac{1}{2}ab-\dfrac{1}{5}ba\right)+\left(\dfrac{1}{3}b+\dfrac{1}{6}b\right)-\left(\dfrac{1}{4}c+\dfrac{1}{7}c\right)+\dfrac{1}{8}a\right]$

So,

$\implies\rm abc\left[-\left(\dfrac{ab}{2}+\dfrac{ab}{5}\right)+\left(\dfrac{b}{3}+\dfrac{b}{6}\right)-\left(\dfrac{c}{4}+\dfrac{c}{7}\right)+\dfrac{a}{8}\right]$

So, taking LCM,

$\implies\rm abc\left[\left(-\dfrac{5ab+2ab}{10}\right)+\left(\dfrac{2b+b}{6}\right)-\left(\dfrac{7c+4c}{28}\right)+\dfrac{a}{8}\right]$

$\implies\rm abc\left[\left(-\dfrac{7ab}{10}\right)+\left(\dfrac{3b}{6}\right)-\left(\dfrac{11c}{28}\right)+\dfrac{a}{8}\right]$

$\implies\rm abc\left[-\dfrac{7ab}{10}+\dfrac{b}{2}-\dfrac{11c}{28}+\dfrac{a}{8}\right]$

Taking LCM,

$\implies\rm abc\left[\dfrac{(-7ab\times28)+(b\times140)-(11c\times10)+(a\times35)}{280}\right]$

So,

$\implies\rm abc\left[\dfrac{-196ab+140b-110c+35a}{280}\right]$

Hence,

$\implies\rm\bf abc\left(\dfrac{35a+140b-110c-196ab}{280}\right)$