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Algebraic Expressions and Identities — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSAlgebraic Expressions and Identities3 Marks
Question
Simplify following: $−\frac{1}{2}\text{a}^2\text{b}^2\text{c}+\frac{1}{3}\text{ab}^2\text{c}−\frac{1}{4}\text{abc}^2−\frac{1}{5}\text{cb}^2\text{a}^2\\+\frac{1}{6}\text{cb}^2\text{a}−\frac{1}{7}\text{c}^2\text{ab}+\frac{1}{8}\text{ca}^2\text{b}.$
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Answer

$−\frac{1}{2}\text{a}^2\text{b}^2\text{c}+\frac{1}{3}\text{ab}^2\text{c}−\frac{1}{4}\text{abc}^2−\frac{1}{5}\text{cb}^2\text{a}^2$
$+\frac{1}{6}\text{cb}^2\text{a}−\frac{1}{7}\text{c}^2\text{ab}+\frac{1}{8}\text{ca}^2\text{b}.$
$−\frac{1}{2}\text{a}^2\text{b}^2\text{c}-\frac{1}{5}\text{cb}^2\text{a}^2+\frac{1}{3}\text{ab}^2\text{c}+\frac{1}{6}\text{cb}^2\text{a}−\frac{1}{4}\text{abc}^2$
$-\frac{1}{7}\text{c}^2\text{ab}+\frac{1}{8}\text{ca}^2\text{b}.$
$=\big(\frac{−5−2}{10}\big)\text{a}^2\text{b}^2\text{c} +\big(\frac{2+1}{6}\big)\text{ab}^2\text{a}^2$
$+\big(\frac{−7−4}{28}\big)\text{c}^2\text{ab}+\frac{1}{8}\text{ca}^2\text{b}$ (Collecting like terms) $=−\frac{7}{10}\text{a}^2\text{b}^2\text{c}+\frac{1}{2}\text{ab}^2\text{c}−\frac{11}{28}\text{abc}^2+\frac{1}{8}\text{a}^2\text{bc} $ (Combining like terms)

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