Sure! Let's solve $3x^4(2x^2 - 1)$ step by step using the distributive property.

We have:

$3x^4(2x^2 - 1)$

Step 1: Distribute the $3x^4$ to both terms inside the parentheses.

• First, multiply $3x^4$ by $2x^2$: $3x^4 \times 2x^2 = 6x^{4+2} = 6x^6$ (Remember that when multiplying exponents with the same base, you add the exponents.)

• Then, multiply $3x^4$ by $-1$: $3x^4 \times (-1) = -3x^4$

Step 2: Combine the results.

Now we put both terms together:

$6x^6 - 3x^4$

So, the simplified expression is:

$6x^6 - 3x^4$

Let me know if you'd like further explanations, or if you have any other questions!

Here are some related questions you might want to explore:

1. How do you apply the distributive property to polynomial expressions?
2. What happens when you multiply exponents with the same base?
3. How do you simplify higher-degree polynomial expressions?
4. How do you factor polynomial expressions like $6x^6 - 3x^4$?
5. What is the difference between simplifying and expanding polynomials?

Tip: Always remember to add the exponents when multiplying powers with the same base.