BUILT-IN MATHEMATICA SYMBOL

Distribute

distributes f over Plus appearing in any of the

.

Distribute

distributes over g.

Distribute

performs the distribution only if the head of expr is f.

MORE INFORMATION

Distribute effectively implements the distributive law for operators f and g.

Distribute explicitly constructs the complete result of a distribution; Expand, on the other hand, builds up results iteratively, simplifying at each stage.

Distribute gives gp and fp in place of g and f respectively in the result of the distribution. »

EXAMPLES

CLOSE ALL

Basic Examples (3)

Apply the distributive law:

Distribute

over Plus:

Distribute

over

:

Apply the distributive law:

In[1]:=

Out[1]=

Distribute

over Plus:

In[1]:=

Out[1]=

Distribute

over

:

In[1]:=

Out[1]=

Scope (4)

By default, distribute over Plus:

Distribute only a product of sums:

Distributive laws for logical operators:

Apply the distributive law to arbitrary operators:

Generalizations & Extensions (1)

Distribute

over

to give

and

:

Applications (5)

Expand symbolic matrix and vector expressions:

Apply the distributive law with any operator:

Find the list of all possible combinations of elements:

Generate a powerset:

Find intermediate terms from a direct application of the distributive law:

Properties & Relations (3)

For pure products, Distribute gives the same results as Expand:

PowerExpand corresponds to distribution over Times:

Outer forms the same combinations of all elements, but in a nested structure:

Neat Examples (1)

Find all possible sums of sublists of a list: