Answer :
To simplify the expression [tex]\(9x^2(4x + 2x^2 - 1)\)[/tex], let's distribute [tex]\(9x^2\)[/tex] to each term inside the parentheses. Here's the step-by-step process:
1. Distribute [tex]\(9x^2\)[/tex] to each term:
- Multiply [tex]\(9x^2\)[/tex] by [tex]\(4x\)[/tex]:
[tex]\[
9x^2 \times 4x = 36x^3
\][/tex]
- Multiply [tex]\(9x^2\)[/tex] by [tex]\(2x^2\)[/tex]:
[tex]\[
9x^2 \times 2x^2 = 18x^4
\][/tex]
- Multiply [tex]\(9x^2\)[/tex] by [tex]\(-1\)[/tex]:
[tex]\[
9x^2 \times (-1) = -9x^2
\][/tex]
2. Combine the results:
Now, write the expression with all terms:
[tex]\[
18x^4 + 36x^3 - 9x^2
\][/tex]
So, the correct simplification of [tex]\(9x^2(4x + 2x^2 - 1)\)[/tex] is:
[tex]\[
18x^4 + 36x^3 - 9x^2
\][/tex]
This matches the first option in the given choices.
1. Distribute [tex]\(9x^2\)[/tex] to each term:
- Multiply [tex]\(9x^2\)[/tex] by [tex]\(4x\)[/tex]:
[tex]\[
9x^2 \times 4x = 36x^3
\][/tex]
- Multiply [tex]\(9x^2\)[/tex] by [tex]\(2x^2\)[/tex]:
[tex]\[
9x^2 \times 2x^2 = 18x^4
\][/tex]
- Multiply [tex]\(9x^2\)[/tex] by [tex]\(-1\)[/tex]:
[tex]\[
9x^2 \times (-1) = -9x^2
\][/tex]
2. Combine the results:
Now, write the expression with all terms:
[tex]\[
18x^4 + 36x^3 - 9x^2
\][/tex]
So, the correct simplification of [tex]\(9x^2(4x + 2x^2 - 1)\)[/tex] is:
[tex]\[
18x^4 + 36x^3 - 9x^2
\][/tex]
This matches the first option in the given choices.