CHAPTER VI.
Removal and Insertion of Brackets..
64. We frequently find it necessary to enclose within brackets part of an expression already enclosed within brackets. For this purpose it is usual to employ brackets of different forms. The brackets in common use are ( ), {}, [ ]. Sometimes a line called a vinculum is drawn over the symbols to be connected; thus a -b+c is used with the same meaning as a-(b+ c), and hence
a-b+c=a-b-c.
65. To remove brackets it is usually best to begin with
the inside pair, and in dealing with each pair in succession we apply the rules already given in Arts. 25, 26.
Ex. 1. Simplify, by removing brackets, the expression a-2b-[4a-6b-{3a-c+(5a-2b-3a-c+2b)}].
Removing the brackets one by one, we have a-2b-[4a-6b-{3a-c+(5a-2b-3a+c-2b)}] =a-2b-[4a-6b-{3a-c+5a-2b-3a+c-2b}] =a-2b-[4a-6b-3a+c-5a+2b+3a-c+2b}] =a-2b-4a+6b+3a-c+5a-2b-3a+c-2b}] = 2a, by collecting like terms.
Ex. 2. Simplify the expression -[-2x-{3y-(2x-3y)+(3x-2y)}+ 2x].
The expression =-[-2x-{3y-2x+3y+3x-2y}+ 2x] =-[-2x-3y+2x-3y-3x+2y- 2x] =2x+3y-2x+3y+3x-2y+ 2x] =x+4y.
