Absolute Value and the Distributive PropertyDate: 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/ |
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