Page:Elementary algebra (1896).djvu/29

Rh 22. Addition is the process of finding in simplest form the algebraic sum of any number of quantities.

23. Like terms, or similar terms, do not differ, or differ only in their numerical coefficients. Other terms are called unlike, or dissimilar. Thus $$3a$$, $$7a$$; $$5a^2b$$, $$2a^2b$$; $$3a^3b^2$$, $$-4a^3b^2$$ are pairs of like terms;and $$4a$$, $$3b$$; $$7a^2$$, $$9a^2b$$ are pairs of unlike terms.

Rule I. The sum of a number of like terms is a like term.

Rule II. If all the terms are positive, add the coefficients.

Rule III. If all the terms are negative, add the coefficients numerically and prefix the minus sign to the sum.

Rule IV. If the terms are not all of the same sign, add together separately the coefficients of allthe positive terms and the coefficients of all the negative terms; the difference of these two results, preceded by the sign of the greater, will give the coefficient of the sum required.