Math 017 Materials With Exercises

For instance, the area of a rectangle is equal to the product LW where L represents its length and Wits width. Let us consider a rectangle with the length and width equal to each other. Recall that thistype of a rectangle is called a square. Let a denote the side of the square. We have W a,L a . Wecan express the area of a square in terms of a . To this end, we replace both W and L with a :2LW aa aAnd thus the area of a square is equal to the square of its side.Now, if for example, we would like to fine the area of a square, whose side is 2 inches long, wedetermine that a 2 (side is 2 inches long), and the area can be found by evaluatinga2 2 2 4The area of the square is 4 (actually 4 in 2 ).Example 7.5 Ifx z, express the following expressions in terms of z.2a) x b) xSolution:2 2 2a) x ( z) zb) x (z) z22Example 7.6 Express ( m n)(m mn n ) in terms ofa) x , if m 2, and n 3x.b) m , if n m.Solution:a) We replace m with 2, and n with 3 x , and simplify.22222( m n)(m mn n ) (2 3x)(2 2(3x) (3x)) (2 3x)(4 6x 3 x2 (2 3x)(4 6x 9x)b) We replace n with m , and simplify.22222 2 22( m n)(m mn n ) ( m m)(m mm m ) 2m(m m m ) 2mm 2m2)3Example 7.7 If2A vandB 2 2v, express ( A B)(A B ) in terms of v .Solution:We must find an equivalent form of the above expression expressed only in terms of2and B . We will remove parentheses.22 2 2( A B)(A B) A AB BA B A B .22Now, we can replace A with v , B with 2 v to get2 2( A B)(A B) A B v 2v v.2AEx.1 If x2 10, evaluate the following.Exercises with Answers (For answers see Appendix A)72