Factoring vs. Simplifying
Date: 03/02/2003 at 19:33:05 From: Mike Subject: Algebra (factoring) Factor the expression 1+y(1+x)^2(1+xy). It looks pretty factored in this form, and I can't figure out how to factor it any further.
Date: 03/03/2003 at 12:43:23 From: Doctor Ian Subject: Re: Algebra (factoring) Hi Mike, It's pretty simplified, but that's not the same as factored. An expression is factored if it contains only factors. For example, y(1 + x)^2(1 + xy) is factored. Why do we make this distinction? Often we're looking for situations where we have 0 = some factored expression This is convenient, because we can then quickly see what the values of the factors have to be. If 0 = y(1 + x)^2(1 + xy) then one of the following must be true: 1) y = 0 2) (1 + x) = 0, i.e., x = -1 3) (1 + xy) = 0, i.e., xy = -1 So to factor your expression, you'd need to expand it out, gather up like terms, and try to factor the result, using the methods you've been learning over the years. Here's a simple example of how that would look: -1 + (x+2)^2 = -1 + (x^2 + 4x + 4) = x^2 + 4x + (4 + -1) = x^2 + 4x + 3 = (x+1)(x+3) Yours will be a little trickier. Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
Date: 03/03/2003 at 21:10:18 From: Mike Subject: Thank you (Algebra (factoring)) Your advice was appreciated, it gave me the help I needed to solve the problem. The answer ended up being: (x^2y+xy+1)(xy+y+1)
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