Page:Elementary algebra (1896).djvu/32

14 $$8 + (13 - 5)$$ means that to 8 we are to add the excess of 13 over 5; now if we add 13 to 8 we have added 5 too much, and must therefore take 5 from the result.

Similarly $$a + (b - c)$$ means that to $$a$$ we are to add $$b$$, diminished by $$c$$.

Thus

In like manner,

Conversely,

therefore

By considering the results $$, $$, $$, $$, we are led to the following rule:

Rule. When an expression within brackets is preceded by the sign $$+$$, the brackets can be removed without making any change in the expression.

Conversely: Any part of an expression may be enclosed within brackets and the sign $$+$$ prefixed, the sign of every term within the brackets remaining unaltered.

Thus the expression $$a - b + c - d + e$$ may be written in any of the following ways,

26. The expression $$a - (b + c)$$ means that from $$a$$ we are to take the sum of $$b$$ and $$c$$. The result will be the same whether $$b$$ and $$c$$ are subtracted separately or in one sum.