Question

Remove the brackets and simplify: $\frac{2}{3}(2a-b)+\frac{1}{2}(a-2b+c)-\frac{1}{3}c$

Answer 1

SImplifying the algebraic expression

Simplification rule: If there is a $"-"$ sign before a bracket, then the signs of all the terms inside the bracket changes but if there is a $“+”$ sign before the bracket, then no change of signs.

$\begin{array}{rcl}\frac{2}{3}(2a-b)+\frac{1}{2}(a-2b+c)-\frac{1}{3}c& =& \frac{4a}{3}-\frac{2b}{3}+\frac{a}{2}-b+\frac{c}{2}-\frac{c}{3}\\ & =& \frac{4a}{3}+\frac{a}{2}-\frac{2b}{3}-b+\frac{c}{2}-\frac{c}{3}\\ & =& \frac{8a+3a}{6}-\frac{2b-3b}{3}+\frac{3c-2c}{6}\\ & =& \frac{11a}{6}-\frac{5b}{3}+\frac{c}{6}\end{array}$

Therefore, the simplified expression is $\frac{11a}{6}-\frac{5b}{3}+\frac{c}{6}$.