Armadillo Run forum

I see Ike is on here.

Hey Ike,

how would you factor x^4-(a^2)(x^2)+16a^4 ?

It looks like a simple binomial squared but the " -a2x2 " has me stumped. how can you possibly get this?

If you take u=x^2 and w=a^2 you get u^2 - wu + 16w^2

That doesn't seem factorable :/

I'll keep looking at it though

Ikerous wrote:If you take u=x^2 and w=a^2 you get u^2 - wu + 16w^2

That doesn't seem factorable :/

I'll keep looking at it though

There are others, but that is the most irritating one...

You can post them. I might fail less at those than this one.

Ikerous wrote:You can post them. I might fail less at those than this one.

=D yay!

x^8 + x^3

I got x^3(x^5 +1), but that just feels wrong.


Same with x4y2 + 2x3y2 + x2y2 - x2y4

I factored out x2y2 and got x2y2(x2 + 2x + 1 - y2), which is ugly :{

And I don't even know where to begin with x^(2a+1) + x^(a+1) - 6x

Answer/don't answer any you want (or don't want) to.

JustcallmeDrago wrote:

Ikerous wrote:You can post them. I might fail less at those than this one.

=D yay!

x^8 + x^3

I got x^3(x^5 +1), but that just feels wrong.


Same with x4y2 + 2x3y2 + x2y2 - x2y4

I factored out x2y2 and got x2y2(x2 + 2x + 1 - y2), which is ugly :{

And I don't even know where to begin with x^(2a+1) + x^(a+1) - 6x

Answer/don't answer any you want (or don't want) to.

I'd say that's as factored as the first one gets. The second one might be able to go a little farther with x^2 y^2 [(x+1)^2 - y^2]
Which would go to x^2 y^2 (x+1-y)(x+1+y)

As for the last one you can factor out an x^(a+1) and get x^(a+1) [x^a + 1] - 6x

for #3 I can't believe i didn't realize x^2a+1 is similar to a normal exponent.

as for #2, that really helped and i see a difference of squares in there. (well, i just saw you edited that in there... but yeah i did find that.

i feel i've done pretty good; i have done 75 of these so far.

how about -(x-y)^2 + c^2 ? nothing is obvious past simplifying... :/

JustcallmeDrago wrote:how about -(x-y)^2 + c^2 ? nothing is obvious past simplifying... :/

You can turn it around and get c^2 - (x-y)^2 which makes (c-x+y)(c+x-y)

Ikerous wrote:

JustcallmeDrago wrote:how about -(x-y)^2 + c^2 ? nothing is obvious past simplifying... :/

You can turn it around and get c^2 - (x-y)^2 which makes (c-x+y)(c+x-y)

Oh.

In[1]:= Factor[x^4 - (a^2) (x^2) + 16 a^4]
Out[1]= (4 a^2 - 3 a x + x^2) (4 a^2 + 3 a x + x^2)

TSchultz wrote:In[1]:= Factor[x^4 - (a^2) (x^2) + 16 a^4]
Out[1]= (4 a^2 - 3 a x + x^2) (4 a^2 + 3 a x + x^2)

so how did you get that?

Mathematica.

TSchultz wrote:Mathematica.

Is it free? or does it show you the steps?

For me it was free. It's free for all BU students, and all students at my high school have BU ID's so we can get it. But otherwise it costs a fair bit (100+ depending on if you're a student or not I think).
And sorry :/ doesn't show the steps. But there's an add on package that does I think.

TSchultz wrote:For me it was free. It's free for all BU students, and all students at my high school have BU ID's so we can get it. But otherwise it costs a fair bit (100+ depending on if you're a student or not I think).
And sorry :/ doesn't show the steps. But there's an add on package that does I think.

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