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The Maxima on-line user's manual

Algebra Calculator

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Expand Calculator

Expand

Function: expand (<expr>)

f1(x):=(x-3*%i)*(x+3*%i)*(x-%i)*(x+%i);
f1(x),expand;
f2(x):=(x-3)*f1(x);
f2(x),expand;
f3(x):=(x-3)*(x+3)*(x-%i)*(x+%i);
f3(x),expand;
f4(x):=(x-1)*f3(x);
f4(x),expand;
f5(x):=(x-5)*(x-2)*(x+1)*(x+3);
f5(x),expand;
f6(x):=x*f5(x);
f6(x),expand;
f7(x):=x! - 2^x;
LOAD(CGAMMA);
f8(x) := Gamma.logGamma( x + 1 ) - x * Log(2);
 solve(p4(x)=0,x);
find_root(f8(x), x, 0.1, 5);
Gamma.logGamma(5.0)

Function: expand (<expr>, <p>, <n>) Expand expression <expr>. Products of sums and exponentiated sums are multiplied out, numerators of rational expressions which are sums are split into their respective terms, and multiplication (commutative and non-commutative) are distributed over addition at all levels of <expr>.

For polynomials one should usually use ratexpand which uses a more efficient algorithm.

maxnegex and maxposex control the maximum negative and positive exponents, respectively, which will expand.

expand (<expr>, <p>, <n>) expands <expr>, using <p> for maxposex and <n> for maxnegex. This is useful in order to expand part but not all of an expression.

expon - the exponent of the largest negative power which is automatically expanded (independent of calls to expand). For example if expon is 4 then (x+1)^(-5) will not be automatically expanded.

expop - the highest positive exponent which is automatically expanded. Thus (x+1)^3, when typed, will be automatically expanded only if expop is greater than or equal to 3. If it is desired to have (x+1)^n expanded where n is greater than expop then executing expand ((x+1)^n) will work only if maxposex is not less than n.

expand(expr, 0, 0) causes a resimplification of expr. expr is not reevaluated. In distinction from ev(expr, noeval) a special representation (e. g. a CRE form) is removed. See also ev.

The expand flag used with ev causes expansion.

The file simplification/facexp.mac contains several related functions (in particular facsum, factorfacsum and collectterms, which are autoloaded) and variables (nextlayerfactor and facsum_combine) that provide the user with the ability to structure expressions by controlled expansion. Brief function descriptions are available in simplification/facexp.usg. A demo is available by doing demo("facexp").

     Examples:
          (%i1) expr:(x+1)^2*(y+1)^3;
                                                2        3
          (%o1)                          (x + 1)  (y + 1)
          (%i2) expand(expr);
                 2  3        3    3      2  2        2      2      2
          (%o2) x  y  + 2 x y  + y  + 3 x  y  + 6 x y  + 3 y  + 3 x  y
                                                           2
                                          + 6 x y + 3 y + x  + 2 x + 1

          (%i3) expand(expr,2);
                                2        3              3          3
          (%o3)                x  (y + 1)  + 2 x (y + 1)  + (y + 1)

          (%i4) expr:(x+1)^-2*(y+1)^3;
                                                    3
                                             (y + 1)
          (%o4)                              --------
                                                    2
                                             (x + 1)
          (%i5) expand(expr);
                           3               2
                          y             3 y            3 y             1
          (%o5)      ------------ + ------------ + ------------ + ------------
                      2              2              2              2
                     x  + 2 x + 1   x  + 2 x + 1   x  + 2 x + 1   x  + 2 x + 1

          (%i6) expand(expr,2,2);
                                                    3
                                             (y + 1)
          (%o6)                            ------------
                                            2
                                           x  + 2 x + 1

Resimplify an expression without expansion:

          (%i7) expr:(1+x)^2*sin(x);
                                                 2
          (%o7)                           (x + 1)  sin(x)
          (%i8) exponentialize:true;
          (%o8)                                true
          (%i9) expand(expr,0,0);
                                             2    %i x     - %i x
                                   %i (x + 1)  (%e     - %e      )
          (%o9)                  - -------------------------------
                                                  2

There are also some inexact matches for expand. Try ?? expand to see them.

(%o1)                                true
(%i2) 

Expand Example

Related Examples

expand

f:expand((x^2)/k*(1/x...

Calculate

expand

a: (y+1)^3/(x+1)^2;

expand(a);

expand(a,2,2);

Calculate

expand

expand(w*x+x*(l-2*x)+...

Calculate

expand-fullratsimp

y(xx,x) := (((x2-x1)*...

z : fullratsimp(expan...

Calculate

expand

exp1:(x+1)^3*(x+2)^2;

expand(expr);

Calculate

expand-kill

kill(all);

c:d+c1;

b:c+b1;

Calculate

expand

expand((2*x-3)^3);

Calculate

expand-float-solve

eq1:8*0.9/(3*v-1)-3/v...

Realpart(float(expand...

Calculate

expand-solve

L0(x):=(x-0.2)*(x-0.4...

L1(x):=(x-0)*(x-0.4)*...

L2(x):=(x-0)*(x-0.2)*...

Calculate