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