Removing
Parenthesis Using Distributive Law
Distributive
Law asserts that
, where a, b, and c are any real numbers.
In general,
we write the distributive law as ,
where the multiplication sign "." is omitted. Note that
in algebra, the multiplication sign is written only for multiplication
of numbers, e.g. .
We apply Distributive
Law from the left to the right to remove parenthesis.
Taking
we get the following two short cuts :
This means
that
1) Parenthesis
precedes by a " +" sign can be simply erased (they
are superfluous parenthesis).
2) Parenthesis
precedes by a "" sign can be removed including the
"" sign and replacing each term to its opposite.
Ex
1:
Remove parenthesis and simplify.
Ex
2: Remove parenthesis and simplify
Ex
3: Remove parenthesis and
simplify
Ex
4:
Remove parenthesis and simplify
Sometimes
this rule for the product of two binomials is called FOIL method.
The Distributive
Law can be generalized as:
that is, you
add the product of every term in the first parenthesis times every
term in the second one.
Ex
5: Remove parenthesis
and simplify
Ex
6:
Remove parenthesis and simplify
Ex
7: Remove parenthesis
and simplify
If we rewrite
the equation as a · b + a · c = a · (b +
c), then this means we factor the common factor out, transforming
the addition into multiplication. This procedure is very
useful in factoring polynomial.
Ex
8: Factor and simplify
For more example
of factoring, click here.
