Which is more 'simple'?Date: 09/24/2001 at 15:27:29 From: Pam Brislin Subject: Which is more 'simple"? My class is trying to figure out which is considered more simple (when simplifying): 2x + 2y (two terms and three operations) or 2(x + y) (one term and two operations, but the higher operation of parentheses). Thanks! Pam Date: 09/24/2001 at 22:19:41 From: Doctor Peterson Subject: Re: Which is more 'simple"? Hi, Pam. I often wonder the same thing; when we get questions about simplification out of context, it's hard to be sure what form is expected. My own sense of the matter is that "simplicity" is in the eye of the beholder - and more specifically, in the context of the problem. We simplify an expression for a reason: to make the next step easier. In some cases, the next step is just to evaluate the expression for particular values, and then the form with the fewest operations may be best (unless those operations involve division by an irrational number, in which case we prefer a rationalized denominator despite a larger number of operations). Other times, we are going to be doing something "additive," such as looking for a polynomial, and your first form is better; or we are going to be doing something "multiplicative," and the factored form is best. If a student asked me for help simplifying this, and I chose to actually show the final answer rather than just pointing her in the general direction, I would probably choose the polynomial form; everything from the order of operations rules up is built around a preference for that form and an avoidance of parentheses, so without context I naturally tend in that direction. But I'll still wonder whether it's really right ... - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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