Math 017 Materials With Exercises

Lesson 7__________________________________________________________________________________Topics:Evaluation of more complicated algebraic expressions; Substitution of not only numbersbut also algebraic expressions.__________________________________________________________________________________Recall,If two quantities are equal, you can always substitute one for the other.“equals can be substituted for equals”Substitution of numbers for entire parts of expressionsAccording to the principle “equals can be substituted for equals” not only can we substitute numbersfor variables, but also for entire „parts of expressions‟.2If, for example, we know that a b 2, we can evaluate ( a b) 3( a b)by substituting the value2 for a b.22( a b) 3( a b) 2 32 4 6 2Example 7.1 Evaluate the expression x y , if 2 x y 0. 2 and z2 0. 4zSolution:x y 0.2 2 z 0.4 4212Using equivalent forms of an algebraic expression for its evaluationIf we are asked to evaluate a „complicated‟ algebraic expression, we may be able to simplify theexpression first, and then use its simplified form to perform the evaluation. Notice, that what we do isreplace („substitute for‟) the original algebraic expression with its equivalent („equal‟) form. Theprinciple “equals can be substituted for equals” is used.Example 7.2 Simplify the expression 3x 3( y x), and then evaluate it when x 3 and y 2.Solution:3x 3( y x) 3x 3y 3x 3x 3x 3y 3yIf y 2, then 3y 3( 2) 6.Sometimes, the only way to perform the evaluation is to first replace the expression with a certainequivalent form of it. Suppose, for example, that we know that x 5, and y z 4 . Is it possible to70