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### 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))

to solve the problem.  The answer ended up being:
(x^2y+xy+1)(xy+y+1)
```
Associated Topics:
High School Basic Algebra
Middle School Algebra
Middle School Factoring Expressions

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