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
+
2
ø
x
ø
y
+
2
ø
x
+
y
+
2
ø
y
+
expand((x^2
ì
x+y^2
ì
y)/(x^2
ù
y^2
ì
x^2
ù
y
ì
x
ù
y^2+x
ù
y
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)
¸
y
ñ
+
2
ø
y
ø
(x
+
1)
+
(x
+
1)
ñ
expand((x+y+1)^2,x)
¸
x
ñ
+
2
ø
x
ø
(y
+
1)
+
(y
+
1)
ñ
expand((x^2
ì
x+y^2
ì
y)/(x^2
ù
y^2
ì
x^2
ù
y
ì
x
ù
y^2+x
ù
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^2
ì
2)/(x^2
ì
2))
¸
2
ø
x
x
ñì
2
+
x+1
expand(ans(1),x)
¸
x
ì
‡2
+
x+‡2
+
x+1
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