Function: expands - symbolic version of expand

Calling sequences:

expands(expr);

Parameters:

expr - the expression to be expanded.

Description:

Examples:

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 where is an integer.

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

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

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

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

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

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)));

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

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