Learning Guide Learning Guide

150 • Chapter 5: Evaluation and Simplification(z + 2) y x + zSection 5.3 explains the use of the subs command.If you are collecting coefficients of more than one variable simultaneously,two options are available, the recursive and distributed forms.Recursive form initially collects in the first specified variable, then in thenext, and so on. The default is the recursive form.> poly := x*y + z*x*y + y*x^2 - z*y*x^2 + x + z*x;poly := y x + z x y + y x 2 − z y x 2 + x + z x> collect( poly, [x,y] );(1 − z) y x 2 + ((1 + z) y + 1 + z) xDistributed form collects the coefficients of all variables at the sametime.> collect( poly, [x,y], distributed );(1 + z) x + (1 + z) y x + (1 − z) y x 2The collect command does not sort the terms. Use the sort commandto sort. See this section, page 160.Factoring Polynomials and Rational FunctionsYou may want to write a polynomial as a product of terms of smallestpossible degree. Use the factor command to factor polynomials.> factor( x^2-1 );(x − 1) (x + 1)> factor( x^3+y^3 );(x + y) (x 2 − y x + y 2 )You can also factor rational functions. The factor command factorsboth the numerator and the denominator, then removes common terms.