SOLUTION: I'm not really sure if this is an appropriate place to put this, since this is a precalculus question. Anyways, if you can help me solve this problem, thanks. Factor using the b

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I'm not really sure if this is an appropriate place to put this, since this is a precalculus question. Anyways, if you can help me solve this problem, thanks. Factor using the b      Log On


   

Question 972841: I'm not really sure if this is an appropriate place to put this, since this is a precalculus question. Anyways, if you can help me solve this problem, thanks.
Factor using the binomial theorem
X^12 + 4x^9(y^3) + 6x^6(y^6) + 4x^3(y^9) + y^12
I hope that's readable. This was a question on my test, and I had no idea what to do. I got (x+(33/2y))^6, but I don't remember how I got it. Either way, my answer's wrong. Finals are coming up, and this question might be on it. Again, thanks.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Your first clue is to look at the coefficients of your given polynomial:



Which are

And this looks exactly like either the Number 4 row of Pascal's Triangle, or the sequence



one of which I will hope makes sense based on your particular understanding of the binomial theorem. Given that, we know from the binomial theorem that



Let's use a substitution to turn your original mud fence into something not quite so butt ugly.

Let and

Now substitute. Since and and (and similarly for the terms), we can substitute and into your original polynomial to get:



which we know from earlier to be equal to:



Now just substitute back again to get:



John

My calculator said it, I believe it, that settles it