anonymous
  • anonymous
Find the term that contains y^8 in the expansion of (2x+y^2)^6
Mathematics
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anonymous
  • anonymous
Find the term that contains y^8 in the expansion of (2x+y^2)^6
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
\[y ^{8}\] \[(2x+y^{2})^{6}\]
Rogue
  • Rogue
Binomial theorem ;)
anonymous
  • anonymous
Would it turn out to be \[y ^{8}=(y ^{2})^{U}\]

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anonymous
  • anonymous
My class hasn't covered logarithms yet, so I'm not sure if it's a guess 'n check type of thing.
Rogue
  • Rogue
Banging it out and multiplying will be extremely tedious. There's a simpler way to do it by using binomial theorem, but that is far too much explaining for now if you haven't already learned it. Does anyone have any other ideas?
anonymous
  • anonymous
I guess you could make an equation out of the exponents 8=2U...
anonymous
  • anonymous
\[\left(2 x+y^2\right)^6=64 x^6+192 x^5 y^2+240 x^4 y^4+160 x^3 y^6+60 x^2 y^8+12 x y^{10}+y^{12} \]

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