Answer :
To simplify the expression [tex]\(9x^2(4x + 2x^2 - 1)\)[/tex], follow these steps:
1. Distribute [tex]\(9x^2\)[/tex] across the terms inside the parentheses:
- Multiply [tex]\(9x^2\)[/tex] by [tex]\(4x\)[/tex]:
[tex]\[
9x^2 \cdot 4x = 36x^3
\][/tex]
- Multiply [tex]\(9x^2\)[/tex] by [tex]\(2x^2\)[/tex]:
[tex]\[
9x^2 \cdot 2x^2 = 18x^4
\][/tex]
- Multiply [tex]\(9x^2\)[/tex] by [tex]\(-1\)[/tex]:
[tex]\[
9x^2 \cdot (-1) = -9x^2
\][/tex]
2. Combine all the terms together:
[tex]\[
18x^4 + 36x^3 - 9x^2
\][/tex]
Therefore, the correct simplification of the expression [tex]\(9x^2(4x + 2x^2 - 1)\)[/tex] is:
[tex]\[
\boxed{18x^4 + 36x^3 - 9x^2}
\][/tex]
This matches with the first option listed in your question choices.
1. Distribute [tex]\(9x^2\)[/tex] across the terms inside the parentheses:
- Multiply [tex]\(9x^2\)[/tex] by [tex]\(4x\)[/tex]:
[tex]\[
9x^2 \cdot 4x = 36x^3
\][/tex]
- Multiply [tex]\(9x^2\)[/tex] by [tex]\(2x^2\)[/tex]:
[tex]\[
9x^2 \cdot 2x^2 = 18x^4
\][/tex]
- Multiply [tex]\(9x^2\)[/tex] by [tex]\(-1\)[/tex]:
[tex]\[
9x^2 \cdot (-1) = -9x^2
\][/tex]
2. Combine all the terms together:
[tex]\[
18x^4 + 36x^3 - 9x^2
\][/tex]
Therefore, the correct simplification of the expression [tex]\(9x^2(4x + 2x^2 - 1)\)[/tex] is:
[tex]\[
\boxed{18x^4 + 36x^3 - 9x^2}
\][/tex]
This matches with the first option listed in your question choices.
