Math Question

[Alienware_Dude]

Okay, I have an algebra question: when you're factoring the sum or difference of two cubes(I'll say sum here), the formula is X^3 + Y^3=(X+Y)(X^2 - XY + Y^2). My question: where does the 'XY' in the middle come from? I'm confused as hell! If anyone could help me, I'd appreciate it. Thanks.

[antgross@pacbell.net]

Originally Posted by Alienware_Dude Okay, I have an algebra question: when you're factoring the sum or difference of two cubes(I'll say sum here), the formula is X^3 + Y^3=(X+Y)(X^2 - XY + Y^2). My question: where does the 'XY' in the middle come from? I'm confused as hell! If anyone could help me, I'd appreciate it. Thanks.

According to this website, the formula is actually +/- so that would explain the -xy
http://www.math.unt.edu/mathlab/emat...oftwocubes.htm
And this one http://www.purplemath.com/modules/specfact2.htm seems to explain the process. SOrry, it's been 20+ years since high school so this is the best I can do.

"I was told there would be no math"
-Chevy Chase playing President Ford on SNL

[doctorgonzo]

Originally Posted by Alienware_Dude Okay, I have an algebra question: when you're factoring the sum or difference of two cubes(I'll say sum here), the formula is X^3 + Y^3=(X+Y)(X^2 - XY + Y^2). My question: where does the 'XY' in the middle come from? I'm confused as hell! If anyone could help me, I'd appreciate it. Thanks.

What do you mean, "where does it come from?" If you want to see how it works, simply do the long multiplication of (x+y)(x²-xy+y²) on paper. You will see that you get x³+y³. It's no different from factoring 15 into 3×5. Where does the 5 come from? It's just there!

[Alienware_Dude]

Hmmm, I'm still a little confused - if I multiply that on paper, do I multiply X times everything in parentheses, then Y? Sorry if it sounds stupid to you, but I'm just having a difficult time grasping it.

[Litespeed]

I always used the FOIL method here see if this helps:

Here we take a quadratic, usually of the form

ax^2 + bx + c = 0

And try to put it in a form like

(c1 x - d1)(c2 x - d2) = 0

This amounts to guessing, so when it works, this is the fastest factoring method. We can try to systematize the method by multiplying the above out; the result is (skipping intermediate steps)

c1 c2 x^2 - (c1 d2 + c2 d1)x + d1 d2 = 0

For most people, this is not very helpful. We will use this expression as a guide to guessing the numbers c1, c2, d1 and d2.

FOIL, of course, means: First, Outside, Inside, Last - the order of multiplication to expand the double parentheses form. The last two equations above show the beginning and end result of a FOIL calculation.


And this works for all types of factoring. I hope that helped.

[doctorgonzo]

Just pretend that they are normal numbers and do the long multiplication. See the attached file for it written out.