Dictionary for Basic and Intermediate Algebra
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Distributive Law
Removing Parenthesis
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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.

 
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