Question

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

Answer 1

From the simplified form of the expression, the third term on expansion is $54x^2y^6$

Given the expression $(3x + y^3)^4$

• For binomial expansion, the power of 3x will be decreasing while y^3 will be increasing.

On expansion, the resulting expression will be:

• $=(3x + y^3)^4\\=(3x)^4(y^3)^0 + 4 (3x)^3(y^3)^1 + 6(3x)^2(y^3)^2 + 4(3x)^1(y^3)^3 + (3x)^0(y^3)^4$

Simplify the result to have:

• $=81x^4+81x^3y^3+54x^2y^6+12xy^9+y^{12}$

From the simplified form of the expression, the third term on expansion is $54x^2y^6$

Learn more on binomial expansion here: brainly.com/question/13800206