distributes f over Plus appearing in any of the xi.
performs the distribution only if the head of expr is f.
- 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[expr,g,f,gp,fp] gives gp and fp in place of g and f respectively in the result of the distribution. »
Examplesopen allclose all
Basic Examples (3)
Apply the distributive law:
Distribute f over Plus:
Distribute f over g:
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 f over g to give fp and gp:
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:
Possible Issues (1)
This use of Distribute does not give the expected result:
The reason is that the argument is evaluated first and the product vanishes:
Prevent evaluation of the argument before Distribute sees it:
Neat Examples (1)
Find all possible sums of sublists of a list: