To simplify the expression \( 2x^2(3 - 4x)^4 \), we can expand it step-by-step:

1. Start by identifying the two main factors: \( 2x^2 \) and \( (3 - 4x)^4 \).

2. We can’t directly expand \( (3 - 4x)^4 \) without using the binomial theorem, but for now, we leave it in its expanded form. However, you can distribute \( 2x^2 \) over the expression after expanding \( (3 - 4x)^4 \), if required.

Thus, the expression remains as:
\[
2x^2(3 - 4x)^4
\]

Do you want to expand it using the binomial theorem? Let me know if you'd like further details or if you have questions!

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Here are 5 related questions for practice:
1. How do you expand \( (a - b)^n \) using the binomial theorem?
2. What is the derivative of \( 2x^2(3 - 4x)^4 \)?
3. How would you factor \( (3 - 4x)^4 \) if it was part of a larger equation?
4. Can you solve \( 2x^2(3 - 4x)^4 = 0 \) for \( x \)?
5. How does the power rule apply when differentiating polynomials?

**Tip:** When expanding powers of binomials, use the binomial theorem to simplify calculations for higher powers efficiently.

Discover how to expand and simplify the expression 2x^2(3 - 4x)^4 step-by-step using the binomial theorem. This guide covers important algebraic concepts such as polynomial expansion and the power rule, suitable for students in Grades 10-12.

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