To address the given problem, let's follow each step in the process of multiplying and reducing the polynomial [tex]\(4x^2(6x - 1)\)[/tex].
1. Given Expression:
[tex]\[
4x^2(6x - 1)
\][/tex]
2. Distribute [tex]\(4x^2\)[/tex] to each term inside the parentheses:
* The first term inside the parentheses is [tex]\(6x\)[/tex]. Multiply [tex]\(4x^2\)[/tex] by [tex]\(6x\)[/tex]:
[tex]\[
4x^2 \times 6x = 24x^3
\][/tex]
* The second term inside the parentheses is [tex]\(-1\)[/tex]. Multiply [tex]\(4x^2\)[/tex] by [tex]\(-1\)[/tex]:
[tex]\[
4x^2 \times (-1) = -4x^2
\][/tex]
3. Combine the results from the distribution step:
[tex]\[
24x^3 - 4x^2
\][/tex]
This is the fully expanded and reduced form of the polynomial. Therefore, the final single polynomial expression after multiplication is:
[tex]\[
24x^3 - 4x^2
\][/tex]
