Let's expand the given expression:

$(4x^3 + y^3)^2$

We apply the formula for squaring a binomial:

$(a + b)^2 = a^2 + 2ab + b^2$

In this case, $a = 4x^3$ and $b = y^3$, so:

$(4x^3 + y^3)^2 = (4x^3)^2 + 2(4x^3)(y^3) + (y^3)^2$

Now, let's compute each term:

1. $(4x^3)^2 = 16x^6$
2. $2(4x^3)(y^3) = 8x^3y^3$
3. $(y^3)^2 = y^6$

Putting it all together:

$(4x^3 + y^3)^2 = 16x^6 + 8x^3y^3 + y^6$

This is the expanded form of the polynomial in standard form.

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Would you like further details or have any questions?

Here are 5 related questions to extend this topic:

1. How do you expand a binomial raised to a higher power (e.g., $(a+b)^3$)?
2. What is the standard form of a polynomial, and how is it determined?
3. How does squaring affect the degree of the polynomial?
4. Can you expand and simplify $(2x^2 + 3y)^2$?
5. How does the distribution property work in polynomial expansion?

Tip: Always ensure the terms in your polynomial are written in decreasing order of their degrees for standard form.