anonymous
  • anonymous
Find the term that contains y^8 in the expansion of (2x+y^2)^6
Mathematics
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
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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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