Function: expands - symbolic version of expand

Calling sequences:



expr - the expression to be expanded.



Both expand and expands produce many of the same expansions.

> expands((x+1)*(x+2));


> expands(sin(x+y));


The expansion of the logarithm of a product. This is not always valid, as there may be an additional term 2*Pi*I*n where n is an integer.

> expand(ln(x*y)),expands(ln(x*y));

ln(x*y), ln(x)+ln(y)

The square root of a product. This is not always valid, as there may be a factor of -1 .

> expand(sqrt(x*y)),expands(sqrt(x*y));

sqrt(x*y), sqrt(x)*sqrt(y)

A power of a power. Again, not always valid (e.g. try it for x = -1 ).

> expand((x^(3/2))^(2/3)), expands((x^(3/2))^(2/3));

(x^(3/2))^(2/3), x

An expandable arctan. expand won't do anything with this, even under conditions that

guarantee its validity.

> assume(x>0,x<1/4,y>0,y<1/4);
expand(arctan((x+y)/(1-x*y))), expands(arctan((x+y)/(1-x*y)));

arctan((x+y)/(1-x*y)), arctan(y)+arctan(x)

A case where expand expands but expands does not. I think it is better to use exp rather than a power of -1 here, to avoid complications with multivalued functions.

> assume(x,real); expand(exp(2*Pi*I*x)), expands(exp(2*Pi*I*x));

(-1)^(2*x), exp(2*I*Pi*x)

See also:

assume , combine , expand

Maple Advisor Database R. Israel 2000