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
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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) (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
^4\ =\ \alpha^4\ +\ 4\alpha^3\beta\ +\ 6\alpha^2\beta^2\ +\ 4\alpha\beta^3\ +\ \beta^4)
Let's use a substitution to turn your original mud fence into something not quite so butt ugly.
Let 
and 
Now substitute. Since ^4)
and ^3)
and ^2)
(and similarly for the 
terms), we can substitute 
and 
into your original polynomial to get:
which we know from earlier to be equal to:
^4)
Now just substitute back again to get:
^4)
John
My calculator said it, I believe it, that settles it
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