Explanation:
In mathematics, and in particular
in abstract algebra, distributivity is a property of binary operations that generalizes the distributive law from elementary algebra. For
example:
2 × (1 + 3) = (2 × 1) + (2 × 3).
4(8+2) = (4×8) + (4×2) because
4(8 + 2) = 4(10) = 40
(4×8) + (4×2) = 32 + 8 = 40
In the
left-hand side of the above equation, the 2 multiplies the sum of 1 and 3; on
the right-hand side, it multiplies the 1 and the 3 individually, with the
results added afterwards. Because these give the same final answer (8), we say
that multiplication by 2 distributes over addition of 1 and 3. Since we could have put any real numbers in place of 2, 1, and 3 above,
and still have obtained a true equation, we say that multiplication of real numbers distributes over addition of real numbers.
Definition
Given a set S and two binary operations · and + on S, we say that the operation ·
1.
is left-distributive over + if, given any elements x, y, and z of S,
x · (y + z) = (x · y) + (x · z); (Our solved example in
mathguru.com uses this concept)
2.
is right-distributive over + if, given any elements x, y, and z of S:
(y + z) · x = (y · x) + (z · x);
3.
is distributive over + if it is both left- and
right-distributive.
http://en.wikipedia.org/wiki/Distributive_property
Commutative property
In mathematics an operation is commutative if changing the order of the operands does not change the end
result. (Our solved example in mathguru.com uses
this concept)
It is a
fundamental property of many binary operations, and many mathematical proofs depend on it. The commutativity
of simple operations, such as multiplication and addition of numbers, was for many years implicitly assumed and the property
was not named until the 19th century when mathematics started to become
formalized. By contrast, division and subtraction are not commutative.
Mathematical
definition
A binary operation ∗ on a set S is said to be commutative if:
(Our solved example in mathguru.com uses
this concept)
An operation
that does not satisfy the above property is called non commutative.
http://en.wikipedia.org/wiki/Commutative_property
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