Page:Elementary algebra (1896).djvu/67

49 Rh EXAMPLES VI. a.

Simplify by removing brackets :

1. a -(b - c)+ a+(b - c)+ b -(c + a). 2. a-[b + {a-(b + a)}]. 3. a-[2a-{3b-(4c-2a)}]. 4. {a - (b - c)] + {b -(c - a)} -{c-(a - b)}. 5. 2a-(5b+[3c-a])-(5a- [b+ c]). 6. -{-[-(a-b -c )}]. 7. -(-(-(- x)))-(-(-y)). 8. -[a-{b -(c - a)}]-['> - {c -(a - b)}]. 9. -[-{-(b + c-a)}] + [-{-(c + a-b)}]. 10. -5x-[3y-{2x -(2y-x)}]. 11. -(-(-a))-(-(-(-x)). 12. 3 a - [a + b - {a + + c -(a + b + c + c?)}]. 13. -2a-[3x + {3c-(4y + 3x + 2a)}]. 14. 3x-[5y-{6z-(4x-7y)}]. 15. -[5x-(11y-3x)]-[5y-(3x-6y)]. 16. -[15x-{14y-(15x+12y)-(10x-15)}]. 17. 8 -{16-[3x-(12-x)-8]+x]. 18. -[x-{z +(x- z)-(z -x)- z}-x]. 19. - [a + {a -(a - x) - (a + x) - a} - a] . 20. - [a - {a + (x - a) -(x -a)-a}- 2 a].

66. A coefficient placed before any bracket indicates that every term of the expression within the bracket is to be multiplied by that coefficient.

Note. The line between the numerator and denominator of a fraction is a kind of vinculum. Thus {x-5}{3} is equivalent to {1}{3}(x - 5).

Again, an expression of the form {x + y) is often written x + y, the line above being regarded as a vinculum indicating the square root of the compound expression x + y taken as a whole.

Thus 25 + 144 = 169 = 13, whereas 26 + 144 = 5 + 12 = 17.

67. Sometimes it is advisable to simplify in the course of the work.