Page:Elementary algebra (1896).djvu/69

51 Rh 19. a-5(b-<a -|{(b - a)-[a-(b-a)]}. 20. 35 [ x -y - {3 x-  (7 x - 4y)}] + 8 (y - 2 x ) . 21. 3. [| (a -b)_ 8 (b-c)}-{b - c - c - a}-{c-a -(a-b) 22. x-(y-z)-[x-{x-(y-z)}-(y-z)-].

INSERTION OF BRACKETS.

68. The converse operation of inserting brackets is important. The rules for doing this have been enunciated in Arts. 25, 26 ; for convenience we repeat them.

Rule I. Any part of an expression may be enclosed ivithin brackets and the sign + prefixed, the sign of every term ivithin the brackets remaining unaltered.

Ex. a — b+c — d — e = a — b+(c — d — e).

Rule II. Any part of an expression may be enclosed icithin brackets and the sign - prefixed, provided the sign of every term ivithin the brackets be changed. Ex. a — b +c — d — e = a —(b — c) — (d + e).

69. The terms of an expression can be bracketed in various ways.

Ex. The expression ax — bx + cx — ay+ by — cy

may be written (ax — bx) + (cx — ay) + (by — cy), or (ax — bx + cx) — (ay — by + cy), or (ax — ay) — (bx — by) + (cx — cy). 70. A factor, common to every term within a bracket, may be removed and placed outside as a multiplier of the expression within the bracket.

Ex. 1. In the expression

ax^3 - cx + 7 - dx^2 +bx-c - dx^3 +bx^2 -2x

bracket together the powers of x so as to have the sign + before each bracket.