Answer:
\(18x^2y^6\) that is option third is correct
Explanation:
We have been given with the expression \((3x+y^3)^4\)
We have general formula for binomial expansion which is
\(a^n +na^{n-1}b+ \frac{(n)(n-1)}{2} a^{n-2}b^2+----------+b^n\)
Here \(a= 3x , b=y^3and\
=4\)
Substituting the values in the formula we will get
\(3x^4+4(3x)^{4-1}y^3+ \frac{(4)(4-1)}{2} 3x^{4-2} (y^{3})^2\\\\ (3x)^4+4(3x)^3y^3+6(3x)^2y^6\\\\(3x)^4+12x^3y^3+18x^2y^6\)+----
we can clearly see that third term of the expansion will be
\(18x^2y^6\)
Therefore, Option third is correct
