# Simplify the Following: − 1 2 a 2 B 2 C + 1 3 a B 2 C − 1 4 a B C 2 − 1 5 C B 2 a 2 + 1 6 C B 2 a − 1 7 C 2 a B + 1 8 C a 2 B . - Mathematics

Simplify the following: $- \frac{1}{2} a^2 b^2 c + \frac{1}{3}a b^2 c - \frac{1}{4}ab c^2 - \frac{1}{5}c b^2 a^2 + \frac{1}{6}c b^2 a - \frac{1}{7} c^2 ab + \frac{1}{8}c a^2 b .$

#### Solution

$- \frac{1}{2} a^2 b^2 c + \frac{1}{3}a b^2 c - \frac{1}{4}ab c^2 - \frac{1}{5}c b^2 a^2 + \frac{1}{6}c b^2 a - \frac{1}{7} c^2 ab + \frac{1}{8}c a^2 b$

$= - \frac{1}{2} a^2 b^2 c - \frac{1}{5}c b^2 a^2 + \frac{1}{3}a b^2 c + \frac{1}{6}c b^2 a - \frac{1}{4}ab c^2 - \frac{1}{7} c^2 ab + \frac{1}{8}c a^2 b$ (Collecting like terms)
= $\left( \frac{- 5 - 2}{10} \right) a^2 b^2 c + \left( \frac{2 + 1}{6} \right)c b^2 a^2 + \left( \frac{- 7 - 4}{28} \right) c^2 ab + \frac{1}{8}c a^2 b$

$= - \frac{7}{10} a^2 b^2 c + \frac{1}{2}a b^2 c - \frac{11}{28}ab c^2 + \frac{1}{8} a^2 bc$        (Combining like terms)

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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 6 Algebraic Expressions and Identities
Exercise 6.2 | Q 7.5 | Page 6