From the simplified form of the expression, the third term on expansion is [tex]54x^2y^6[/tex]
Given the expression [tex](3x + y^3)^4[/tex]
- For binomial expansion, the power of 3x will be decreasing while y^3 will be increasing.
On expansion, the resulting expression will be:
- [tex]=(3x + y^3)^4\\=(3x)^4(y^3)^0 + 4 (3x)^3(y^3)^1 + 6(3x)^2(y^3)^2 + 4(3x)^1(y^3)^3 + (3x)^0(y^3)^4\\[/tex]
Simplify the result to have:
- [tex]=81x^4+81x^3y^3+54x^2y^6+12xy^9+y^{12}[/tex]
From the simplified form of the expression, the third term on expansion is [tex]54x^2y^6[/tex]
Learn more on binomial expansion here: https://brainly.com/question/13800206
