If $A = 3 a - 2 b, B = - 2 a + 3 b$ and $C = - a - b$ .
Find $A + B + C$

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Solution

To add two or more algebraic expressions, group the like terms of the expressions and each group of like terms separately.
The sum
$= (3 a - 2 b) + (- 2 a + 3 b) + (- a - b)$
$= (3 a - 2 a - a) + (- 2 b + 3 b - b)$ (grouping the like terms)
$= (3 - 2 - 1) a + (- 2 + 3 - 1) b$ (adding the numerical coefficient of like terms)
$= (3 - 3) a + (3 - 3) b = 0 a + 0 b = 0$
Hence, the required solution of $A + B + C = 0$

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