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Factoring Cubic Expressions

```Date: 08/24/2010 at 18:25:50
From: katy
Subject: factoring

I don't know how to factor numbers with variables to the third power. For
example, how do I factor this?

16x^3 - 250

```

```
Date: 08/25/2010 at 10:28:34
From: Doctor Ian
Subject: Re: factoring

Hi Katy,

The first thing I'd do is look for other cubes.

For example, I can write your cubic expression this way:

2(8x^3 - 125)

= 2(2^3 x^3 - 5^3)

= 2((2x)^3 - 5^3)

What might you try next?

Now, if you're not particularly facile with cubes, you could make things a
little more visible by finding prime factors, and expanding exponents. For
example,

16x^3 - 250

= 2*2*2*2*x*x*x - 2*5*5*5
|___| |___|     |___|
|_____|_________|______  Here are the cubes!

In some ways, prime factors are a kind of x-ray machine for uncovering
hidden structure in expressions.  :^D

Does this help?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Factoring Expressions

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