Final answer:
The expression (4x^3+3y^3)^5 can be expanded using the binomial theorem. The correct answer is option b) 2y(4x^3+3y^3)^5.
Step-by-step explanation:
The expression (4x^3+3y^3)^5 can be expanded using the binomial theorem. According to the binomial theorem, (a+b)^n = C(n,0)a^n * b^0 + C(n,1)a^(n-1) * b^1 + C(n,2)a^(n-2) * b^2 + ... + C(n,n)a^0 * b^n, where C(n,k) represents the binomial coefficient.
Using this theorem, we can expand (4x^3+3y^3)^5 as:
(C(5,0)(4x^3)^5 * (3y^3)^0) + (C(5,1)(4x^3)^4 * (3y^3)^1) + (C(5,2)(4x^3)^3 * (3y^3)^2) + (C(5,3)(4x^3)^2 * (3y^3)^3) + (C(5,4)(4x^3)^1 * (3y^3)^4) + (C(5,5)(4x^3)^0 * (3y^3)^5).
When you simplify and combine like terms, you will get the expression 2y(4x^3+3y^3)^5, so the correct answer is option b) 2y(4x^3+3y^3)^5.