Question

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Answer 1

The Binomial Expansion Theorem for a binomial elevated to the fourth power is:
`(x+y) ^(4) = x^(4) + 4 x^(3) y + 6 x^(2) y^(2) + 4x y^(3) + y^(4)`
Now lets apply this to our expression:

`(y^(3) +3x)^(4) = y^(12) +12x y^(9)+54 x^(2) y^(6)+108 x^(3) y^(3) +81 x^(4)`
The third term in our binomial expansion is
`54 x^(2) y^(6)`; therefore, the correct answer is the fourth one.