Texas Instruments TI-92 Owners Manual - Page 462

expand() MATH/Algebra menu expand(expression1 [, var]) ⇒ expression expand(list1 [,var]) ⇒ list expand(matrix1 [,var]) ⇒ matrix expand(expression1) returns expression1 expanded with respect to all its variables. The expansion is polynomial expansion for polynomials and partial fraction expansion for rational expressions. expand((x+y+1)^2) ¸ xñ + 2ø xø y + 2ø x + yñ + 2ø y + 1 expand((x^2ì x+y^2ì y)/(x^2ù y^2 ì x^2ù yì xù y^2+xù y)) ¸ The goal of expand() is to transform expression1 into a sum and/or difference of simple terms. In contrast, the goal of factor() is to transform expression1 into a product and/or quotient of simple factors. 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^2 ì 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 Appendix A: Functions and Instructions 445