Texas Instruments TI-89 User Manual - Page 818

expand(expression1,var) returns expression expanded with respect to var. Similar powers of var are collected. The terms and their factors are sorted with var as the main variable. There might be some incidental factoring or expansion of the collected coefficients. Compared to omitting var, this often saves time, memory, and screen space, while making the expression more comprehensible. expand((x+y+1)^2,y) ¸ yñ + 2ø yø (x + 1) + (x + 1)ñ expand((x+y+1)^2,x) ¸ xñ + 2ø xø (y + 1) + (y + 1)ñ expand((x^2ì x+y^2ì y)/(x^2ù y^2ì x^2ù yì xù y^2+xù y),y) ¸ expand(ans(1),x) ¸ Even when there is only one variable, using var might make the denominator factorization used for partial fraction expansion more complete. Hint: For rational expressions, propFrac() is a faster but less extreme alternative to expand(). Note: See also comDenom() for an expanded numerator over an expanded denominator. expand((x^3+x^2ì 2)/(x^2ì 2)) ¸ 2ø x xñ ì 2 + x+1 expand(ans(1),x) ¸ 1 xì ‡2 + 1 x+‡2 + x+1 expand(expression1,[var]) also distributes logarithms and fractional powers regardless of var. For increased distribution of logarithms and fractional powers, inequality constraints might be necessary to guarantee that some factors are nonnegative. expand(expression1, [var]) also distributes absolute values, sign(), and exponentials, regardless of var. Note: See also tExpand() for trigonometric angle-sum and multiple-angle expansion. ln(2xù y)+‡(2xù y) ¸ ln(2ø xø y) + ‡(2ø xø y) expand(ans(1)) ¸ ln(xø y) + ‡2ø ‡(xø y) + ln(2) expand(ans(1))|y>=0 ¸ ln(x) + ‡2ø ‡xø ‡y + ln(y) + ln(2) sign(xù y)+abs(xù y)+ e^(2x+y) ¸ e2ø x+y + sign(xø y) + |xø y| expand(ans(1)) ¸ sign(x)øsign(y) + |x|ø|y|+ (ex)2øey expr( ) MATH/String menu expr(string) ⇒ expression Returns the character string contained in string as an expression and immediately executes it. expr("1+2+x^2+x") ¸ xñ + x + 3 expr("expand((1+x)^2)") ¸ xñ + 2ø x + 1 "Define cube(x)=x^3"! funcstr ¸ "Define cube(x)=x^3" expr(funcstr) ¸ Done cube(2) ¸ 8 818 Appendix A: Functions and Instructions