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Simplifying Algebraic Expressions

```
Date: 03/23/2002 at 19:01:45
From: Heidi  Callahan
Subject: Simplifying Algebraic Expressions

I am looking for guidelines to follow when simplifying algebraic
expressions (for simple expressions and more complex expressions).
Are there certain rules to follow?
```

```
Date: 03/27/2002 at 09:12:51
From: Doctor Ian
Subject: Re: Simplifying Algebraic Expressions

Hi Heidi,

In some sense, your algebra textbook is a collection of guidelines for
simplifying expressions. There's not a lot that I'd be able to add to

In my experience, the most useful 'rules' are (1) the distributive
property, and (2) factoring into binomials.

The former allows you to gather together like terms that are
originally separated in an expression. The latter allows you to cancel
this:

x(xy - 4x) - x(y + 4) - 3(2y + 8)
--------------------------------
xy^2 - 16x - 3y^2 + 48

Applying the distributive property allows us to break everything into
monomials. Once we've done that, we can move like monomials together,
and use the distributive property again to factor out shared terms.
The resulting polynomials are candidates for factoring into
polynomials:

(x^2y - 4x2) - (xy + 4x) - (6y + 24)   Distribute multiplications
------------------------------------
xy^2 - 16x - 3y^2 + 48

x^2y - 4x2 - xy - 4x - 6y - 24         Eliminate parentheses
------------------------------
xy^2 - 16x - 3y^2 + 48

x^2y - xy - 6y - 4x2 - 4x - 24         Move like terms together
------------------------------
xy^2 - 16x - 3y^2 + 48

y(x^2 - x - 6) - 4(x2 - x - 6)         Factor
------------------------------
xy^2 - 16x - 3y^2 + 48

y(x+2)(x-3) - 4(x+2)(x-3)           Factor
------------------------------
xy^2 - 16x - 3y^2 + 48

(y-4)(x+2)(x-3)                 Undistribute multiplications
------------------------------
xy^2 - 16x - 3y^2 + 48

(y-4)(x+2)(x-3)
------------------------------
x(y^2 - 16) - 3(y^2 - 16)          Factor

(y-4)(x+2)(x-3)
------------------------------
(x-3)(y^2 - 16)                 Undistribute multiplications

(y-4)(x+2)(x-3)
------------------------------
(x-3)(y+4)(y-4)                 Factor

(x+2)
------------------------------         Cancel
(y+4)

All of which is to say, armed with only these two techniques, you can
go a long, long way. Which would explain why so much emphasis is
placed on them!

or anything else.

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Basic Algebra
High School Polynomials

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