Math 017 Materials With Exercises

Adding and subtracting like termsIf we are to add or subtract objects they must have the same units. For example, we can add dollars todollars and pounds to pounds, but we cannot add dollars to pounds. If we have 3 oranges and 5oranges, together we have 8 oranges, but if we have 3 oranges and 5 plums, we cannot add themtogether. The same idea applies to addition and subtraction of algebraic expressions. Like, and onlylike, terms can be added or subtracted.We apply the Distributive Law to add like terms.3a 5a (3 5) a 8a(or, 3 oranges and 5 oranges equal 8 oranges)To add (or subtract) like terms, add (or subtract) their numerical coefficients and keep nonnumericalfactors the same.For example,Similarly,3x 8x (3 8)x 5x1 3 1 3 4xy yx xy xy7 7 7 7 72 220.3y 0.1y (0.3 0.1) y 0.2y2The process of adding and subtracting like terms is called combining like terms or collecting liketerms.Example 6.2 If possible, collect like terms. Otherwise, write “not possible”.a) 3x 4x1 2 3 2b) a a2 7c) 0.5mn 0. 7mab 1d) ba3 6Solution:a) 3 x 4x ( 3 4)x x1 2 3 2 1 3 2 7 6 2 1 2b) a a a a a2 7 2 7 1414 14c) Since terms mn and m are not like terms, terms cannot be combined. It is“not possible”.ab 1 1 1 1 1 2 1 1d) ba ab ab ab ab ab3 6 3 6 3 6 6 6 662