To simplify the expression \((3x^3 - y^4)^2\), you can apply the square of a binomial formula, which states:

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

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

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

Now, simplify each term:

1. \((3x^3)^2 = 9x^6\)
2. \(-2(3x^3)(y^4) = -6x^3y^4\)
3. \((y^4)^2 = y^8\)

So the fully expanded expression is:

\[
9x^6 - 6x^3y^4 + y^8
\]

Would you like more details on any step?

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Here are some related questions:
1. How would you expand \((2x^2 + 3y^3)^2\)?
2. Can you factor \(9x^6 - 6x^3y^4 + y^8\)?
3. What happens if you set \(x = 1\) and \(y = 1\) in this expression?
4. How do you use the binomial expansion for more than two terms?
5. What is the difference between squaring a binomial and cubing it?

**Tip:** Remember to apply the distributive property when expanding binomials!

Learn how to expand the binomial expression (3x^3 - y^4)^2 using the square of a binomial formula. This step-by-step solution simplifies the expression into 9x^6 - 6x^3y^4 + y^8, covering key algebraic concepts like binomial expansion and exponents. Suitable for students in Grades 9-11.

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