Learning Guide Learning Guide

5.1 Mathematical Manipulations • 157A Special Case Normal may return an expression in expanded formthat is not as simple as the factored form.> expr := (x^25-1) / (x-1);expr := x25 − 1x − 1> normal( expr );1 + x 5 + x 4 + x 3 + x 2 + x 11 + x + x 16 + x 7 + x 10 + x 8 + x 6 + x 9+ x 18 + x 14 + x 19 + x 17 + x 15 + x 12 + x 24 + x 22 + x 23 + x 21+ x 20 + x 13To cancel the common (x − 1) term from the numerator and the denominatorwithout expanding the numerator, use factor. See this section,page 150.> factor(expr);(x 4 + x 3 + x 2 + x + 1) (x 20 + x 15 + x 10 + x 5 + 1)Simplifying ExpressionsThe results of Maple’s simplification calculations can be very complicated.The simplify command tries to find a simpler expression by applying alist of manipulations.> expr := 4^(1/2) + 3;expr := √ 4 + 3> simplify( expr );5> expr := cos(x)^5 + sin(x)^4 + 2*cos(x)^2> - 2*sin(x)^2 - cos(2*x);expr := cos(x) 5 + sin(x) 4 + 2 cos(x) 2 − 2 sin(x) 2 − cos(2 x)> simplify( expr );