Find the term that contains y^8 in the expansion of (2x+y^2)^6

Question

anonymous · Answer

$$y ^{8}$$
$$(2x+y^{2})^{6}$$

rogue · Answer

Binomial theorem ;)

anonymous · Answer

Would it turn out to be $$y ^{8}=(y ^{2})^{U}$$

anonymous · Answer

My class hasn't covered logarithms yet, so I'm not sure if it's a guess 'n check type of thing.

rogue · Answer

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 · Answer

I guess you could make an equation out of the exponents 8=2U...

anonymous · Answer

$$\left(2 x+y^2\right)^6=64 x^6+192 x^5 y^2+240 x^4 y^4+160 x^3 y^6+60 x^2 y^8+12 x y^{10}+y^{12}  $$