Expand and state your answer as a polynomial in standard form.

left parenthesis, 4, x, cubed, plus, y, cubed, right parenthesis, squared

(4*x*3+*y*3)2

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.

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 theorem. This detailed solution covers the expansion process, including the use of the binomial formula, and simplifies the expression into its standard form. Suitable for students in Grades 9-11.

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