Math 017 Materials With Exercises

Commutative Propertyof Additionx y y xAlso, since x y x ( y) y x , we haveConsequence of CommutativeProperty of Additionx y y xEquivalently, we can say that, changing the order of terms results in an equivalent expression (anexpression that looks different, but „means‟ the same). For example,The terms of a 3 are a and 3. If we reverse the order of terms, we obtain a 3 3a .2222The terms of a b are a and b . Reversing their order gives us a b b a .The terms of c 2dare c and 2d. Reversing their order gives us c 2 d 2d c.Similarly, if an algebraic expression consists of more than two terms, we can rearrange them in anyorder. For instance, the terms of 3 B C are 3, B , and C . Thus, we can rewrite the expression3 B C as B C 3 or 3 B C :3 B C B C 3 3B C (there are more possible rearrangements).Example 3.3 Using the fact that changing the order of terms results in an equivalent expression,rewrite the following expressions in their equivalent form by rearranging the terms. Usethe equal sign to indicate that the resulting expressions are equivalent.a) 7 a bb) ( b c)2 3aSolution:a) The terms are 7 a and b . We get 7a b b 7ab) The terms of ( b c)2 2 3aare ( b c) and 3 a . If we reverse the order,we get2( b c) 3a 3a ( b c)2Example 3.4 Determine which of the following expressions are equal to 2x 5y 4z.a) 2x 4z 5yb) 5y 4z 2xc) 5y 2x 4zSolution:All of them are. The terms of 2x 5y 4zare 2x, 5yand 4z. As long as the signthat is in front of an expression is not altered, we can rearrange terms. The sign thatgoes before 2 x is plus, and in all expressions (a)-(c) 2 x is also preceded by a plus sign.5 y follows the minus sign and the same is true for all expressions (a)-(c). Finally, 4zispreceded by a plus sign in all these expressions.26