What is the third term in the binomial expansion of (3x + y³)⁴? 
54x²y³ 
18x²y³
18x²y⁶ 
54x²y⁶

Solution:

Given, the expression is (3x + y³)⁴

We have to find the third term in the binomial expansion.

The general formula for binomial expansion is 

\(a^{n}+na^{n-1}b+\frac{n(n-1)}{2}a^{n-2}b^{2}+............+b^{n}\)

Here, a=3x, b=y³ and n=4

Substituting the values in the formula,

\(3x^{4}+4(3x)^{4-1}y^{3}+\frac{(4)(4-1)}{2}3x^{4-2}(y^{3})^{2}+............\\(3x)^{4}+4(3x)^{3}y^{3}+6(3x)^{2}y^{6}+................\\81x^{4}+108x^{3}y^{3}+54x^{2}y^{6}+.....\)

Therefore, the third term is 54x²y⁶

What is the third term in the binomial expansion of (3x + y³)⁴? 

Summary:

The third term in the binomial expansion of (3x + y³)⁴ is 54x²y⁶.