Answer :

Certainly! Let's go through the problem step by step to simplify the expression:

We have the expression:
[tex]\[ -4x^2(6x^4 - 9x^2) \][/tex]

To simplify, we'll apply the distributive property. This means we'll multiply [tex]\(-4x^2\)[/tex] with each term inside the parentheses.

Step 1: Multiply [tex]\(-4x^2\)[/tex] by [tex]\(6x^4\)[/tex].
- Multiply the coefficients: [tex]\(-4 \times 6 = -24\)[/tex].
- For the [tex]\(x\)[/tex] terms, add the exponents: [tex]\(x^2 \times x^4 = x^{2+4} = x^6\)[/tex].
- The result for this part is [tex]\(-24x^6\)[/tex].

Step 2: Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-9x^2\)[/tex].
- Multiply the coefficients: [tex]\(-4 \times -9 = 36\)[/tex].
- For the [tex]\(x\)[/tex] terms, add the exponents: [tex]\(x^2 \times x^2 = x^{2+2} = x^4\)[/tex].
- The result for this part is [tex]\(36x^4\)[/tex].

Step 3: Combine the results from both steps.
- The expression is now: [tex]\(-24x^6 + 36x^4\)[/tex].

So, the simplified form of the expression is:
[tex]\[ -24x^6 + 36x^4 \][/tex]

That's the final answer! If you have any more questions or need further help, feel free to ask!

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