Why Algebraic Expressions with Parentheses?Date: 03/18/2003 at 10:27:34 From: Jason Subject: Algebraic Expressions Without Parentheses How would you write these algebraic expressions without parentheses? -(2x-3y-6) and -(5x-13y-1) I was told that you can, but I don't think you can without solving the problem. The problem is, there is not enough information there to solve the problem. So, if it is possible to write the expressions without the parentheses, then how do you do it? Also if you can do it, then why are the parentheses there in the first place? Date: 03/18/2003 at 12:48:26 From: Doctor Ian Subject: Re: Algebraic Expressions Without Parentheses Hi Jason, I think you mean that these are expressions, and not equations, so there's no way to determine unique values for x and y. If so, you're absolutely right. One way to write the expressions without the parentheses is to translate -whatever into -1 * whatever since those are equivalent. Let's see what happens when we do that: -(2x-3y-6) = -1 * (2x - 3y - 6) Now we can apply the distributive property: = ((-1)2x - (-1)3y - (-1)6) = (-2x + 3y + 6) After you do this enough times, you'll notice that you can just flip the signs, e.g.: -(5x - 13y - 1) = (-5x + 13y + 1) >Also if you can do >it, then why are the parentheses there in the first place? Sometimes the parentheses are there because the expression came from somewhere else, and had to be substituted as a whole. For example, you might start with something like (number of zibbles) = (number of brizzles) - (number of wilmons) = (3x + 4y - 4) - (5x - 13y + 1) And now your life will be easier if you move the minus sign inside: = (3x + 4y - 4) + (-5x + 13y - 1) because now you can just drop all the parentheses: = 3x + 4y - 4 + -5x + 13y - 1 But just because you had to substitute the expression using parentheses, that doesn't mean you want to keep the parentheses around any longer than you have to. Does that make sense? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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