Expand and state your answer as a polynomial in standard form.
left parenthesis, 4, x, cubed, plus, y, cubed, right parenthesis, squared
(4x 
3
 +y 
3
 ) 
2

We are tasked with expanding and writing the polynomial \((4x^3 + y^3)^2\) in standard form.

To solve this, we can apply the square of a binomial formula:

\[
(a + b)^2 = a^2 + 2ab + b^2
\]

In this case, \(a = 4x^3\) and \(b = y^3\). Applying the formula:

\[
(4x^3 + y^3)^2 = (4x^3)^2 + 2(4x^3)(y^3) + (y^3)^2
\]

Now, calculate 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 polynomial in standard form.

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Would you like more details on any step or further clarification? 

Here are five related questions:
1. What is the square of \((2x^2 + 3y^2)^2\)?
2. How does the binomial expansion formula apply to cubes?
3. Can you expand \((x^2 + y^2)^3\) using a similar approach?
4. What is the general formula for expanding \((a + b)^n\) for any \(n\)?
5. How do you simplify higher-degree polynomials in standard form?

**Tip:** Always simplify the individual terms of your expansion before combining them into the final polynomial.

Expand and state your answer as a polynomial in standard form. (4x^3 + y^3)^2

Learn how to expand and simplify the polynomial (4x^3 + y^3)^2 using the binomial expansion theorem. This problem covers algebraic concepts such as binomial expansion, polynomial simplification, and standard form. Suitable for students in Grades 9-12.

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