Math 017 Materials With Exercises

Example 11.2 The expression( 22 2x 2) ( y 1)3 is written in the form22 2( x p) ( y q) rWhat are the values of p, q, and r ?Solution:Compare22 2( x p) ( y q) r22with ( x 2) ( y 1) 3to find that p 2,q 1, and r 3.2Rewriting expressions in a prescribed formIt is quite often that in order to match expressions we must rewrite a given expression in aprescribed form.Example 11.3 Write the expressiona) x y as a sum of two expressions, that is in the form A B .b) x y as a difference of two expressions, that is in the form A B .Solution:a) The difference of any two expressions always can be written as a sumx y x ( y)b) The sum of any two expressions always can be written as a differencex y x ( y)To see that (a) and (b) are true, recall the rules for signed numbers x ( y) x y ,x ( y) x y . Now, interchange the left-hand side of each of the equations with itsright-hand one (it can always be done!), and we obtain exactly what we claimed in part(a) and (b) of the solutions.22Example 11.4 Write the expression ( x 2) ( y 1)16in the form22 2( x p) ( y q) rWhat are the values of p, q, and r ?Solution:22We rewrite ( x 2) ( y 1)16asCompare( xr22 2 p) ( y q) with22( x ( 2)) ( y ( 1))to find that p 2,q 1,and r 4 .22( x ( 2)) ( y ( 1))4242Example 11.5 Write the following expression in the formEach time identify A .2A , where A is any algebraic expression.106