Subtract $2 a b + 5 b c - 7 a c$ from $5 a b - 2 b c - 2 a c + 10 a b c$ .

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Solution

We have, 2ab + 5bc - 7ac and 5ab - 2bc - 2ac + 10abc
The required difference is given by $(5 a b - 2 b c - 2 a c + 10 a b c) - (2 a b + 5 b c - 7 a c)$
$= 5 a b - 2 b c - 2 a c + 10 a b c - 2 a b - 5 b c + 7 a c$
$= (5 a b - 2 a b) + (- 2 b c - 5 b c) + (- 2 a c + 7 a c) + 10 a b c$ [grouping like terms]
$= 3 a b - 7 b c + 5 a c + 10 a b c$

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