Appendix A: Functions and Instructions 445
8992APPA.DOC TI-89 / TI-92 Plus: Appendix A (US English) Susan Gullord Revised: 02/23/01 1:48 PM Printed: 02/23/01 2:21 PM Page 445 of 132
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.
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((x+y+1)^2) ¸
x
ñ
+ 2øxøy + 2øx + y
ñ
+ 2øy +
1
expand((x^2ìx+y^2ìy)/(x^2ùy^2
ìx^2ùyìxùy^2+xùy
))
¸
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+ 2øyø(x + 1) + (x + 1)ñ
expand((x+y+1)^2,x) ¸
xñ+ 2øxø(y + 1) + (y + 1)ñ
expand((x^2ìx+y^2ìy)/(x^2ùy^2
ìx^2ùyìxùy^2+xùy),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^2ì2)/(x^2ì2))
¸
2øx
xñì2 + x+1
expand(ans(1),x) ¸
1
xì‡2 +
1
x+‡2 + x+1