SUBTRACTION.
33. Subtraction is the inverse of Addition. The simplest cases have been considered under the head of addition of like terms, of which some are negative. [Art. 23.]
Thus 5a-3a= 2 a, 3 a - 7 a = - 4 a, - 3a - 6a = - 9a.
Also, by the rule for removing brackets [Art. 2G], 3 a - (- 8 a)= 3 a +8 a = 11 a,
and - 3 a - (- 8 a)= - 3 a + 8 a = 5a.
SUBTRACTION OF UNLIKE TERMS.
34. The method is shown in the following example :
Ex. Subtract 3a - 2b - c from 4 a - 3 b + 5 c.
The result of subtraction = 4 a - 3 b + 5 c -(3a - 2b - c) = 4a-3b + 5c-3a + 2b + c = 4a-3a-3b + 2b + 5c + c = a-b +6c.
It is, however, more convenient to arrange the work as follows, the signs of all the terms in the lower line being changed.
4a-3b + 5c - 3a + 2b + c by addition a - b + 6 c
Rule. Change the sign of every term in the expression to he subtracted, and add it to the other expression.
Note. It is not necessary that in the expression to be subtracted the signs should be actually changed; the operation of changing signs ought to be performed mentally.
