Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

Absolute Value and the Distributive Property


Date: 12/11/2001 at 20:59:11
From: Ira Campbell
Subject: Absolute Value

Is the distributive property applicable to absolute value?


Date: 12/12/2001 at 10:31:49
From: Doctor Peterson
Subject: Re: Absolute Value

Yes and no. You can't blindly apply it as if the absolute value symbol 
were just a pair of parentheses; but you can prove a sort of 
distributive property using the properties of the absolute value.

Remember that

    |a| * |b| = |ab|

Now let's try to manipulate |a| * |b + c|:

    |a| * |b + c| = |a(b + c)| = |ab + ac|

This is the absolute value equivalent of the distributive property. If 
a is non-negative, you can drop the absolute value around it, and you 
get

    a * |b + c| = |ab + ac|   for a >= 0

But don't forget the condition on a. If a is negative, the left side 
of this is negative, and the right side is positive, which won't work 
well.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Basic Algebra

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/