Math 017 Materials With Exercises

Lesson 11__________________________________________________________________________________Topics: Recognizing and matching patterns; Writing expressions in a prescribed way; Definition ofa linear equation; Factorization of the difference of squares.__________________________________________________________________________________This lesson is devoted to developing the ability to rewrite expressions according to a prescribed rule orpattern, as well as to match variables in the formula with appropriate parts of the expression.Matching expressions2If we are asked to remove parentheses in the expression, let us say ( x 3) , we might do it byremembering that raising an expression to the second power means to multiply it by itself two timesand thus222( x 3) ( x 3)( x 3) x 3x 3x 9 x 6x 9 .Alternatively, in this case, we could recall and use the equation that says that for any two numbers a2 222and b, ( a b) a 2ab b . To this end, we have to match the expression ( x 3) to the left-2hand side of the equation ( a b) and identify a and b in this representation. It might be helpful towrite the two expressions one under the other.2( a b)2( x 3)This makes it easier for us to see that a x and b 3 in this representation. Now, we rewrite theright side of the equation by replacing a with x and b with 3 in the right-hand side of the equation.22a 2ab b x2 2Thus ( x 3) x 6x 9 .2 2x332 x2 6x 9In order to use the formulas, we need to learn how to match expressions.2 xExample 11.1 The expression is written in the formz 1z 1represent a, b, and c, respectively.a cbc. What algebraic expressionsSolution:We matchwithto see that2 xz 1z 1a bc ca 2 , b x , and c z 1.105