Math 017 Materials With Exercises

Lesson 6__________________________________________________________________________________Topics: Addition and subtraction of algebraic expressions.__________________________________________________________________________________In this lesson we will learn how and when to perform the operations of addition and subtraction ofalgebraic expressions.Like terms22Consider 3 x 4y z . The expression consists of three terms: 3x , 4y, z . Each term can beviewed as a product of a numerical and non-numerical factor (recall that numerical factors are alsocalled numerical coefficients). And so,3 x has a numerical factor 3, non-numerical factor x22 4y has a numerical factor 4 , non-numerical factor yz has a numerical factor 1, non-numerical factor zLike TermsLike terms are terms that have equal non-numerical factors.What is meant by non-numerical factors being equal is that they are equal (equivalent) as algebraicexpressions. That does not mean that they „look identical‟. You will notice that in the second examplebelow, xy and yx are equivalent even though they do not „look identical‟.Examples:3 a and 7 a are like terms because their non-numerical factors, both a ‟s, are equivalent.4 xy and 3yxare like terms because xy and yx are equivalent.2x and3x are not like terms since2x is not equivalent toAnother way of looking at like terms is that two terms are alike if they can be written as expressions3 2that have the same variables with the same exponents. For example, 5x y and 4 yx 3 y are like terms,because yx 33 24 y can be written as 4xy , and thus both expressions consist of the variable x raised tothe third power and variable y raised to the second power. It should be stressed once again, that beinglike terms does not mean ‘looking identical’.3x .Example 6.1 Circle all expressions that are like2 34yxyx 3 y23 y3 2x .0 .2( xy)2y2 32xySolution:We should circle3yx y2x y2123 23 2 x y ).2 3 4yx (because2 3 3 2 4yx 4xy ) andyx 3 y2(because61