Answer :
Sure! Let's simplify the expression step-by-step:
We need to simplify the expression [tex]\(9x^2(4x + 2x^2 - 1)\)[/tex].
1. Distribute [tex]\(9x^2\)[/tex] to each term inside the parentheses:
- First, multiply [tex]\(9x^2\)[/tex] by [tex]\(4x\)[/tex]:
[tex]\[
9x^2 \times 4x = 36x^{2+1} = 36x^3
\][/tex]
- Next, multiply [tex]\(9x^2\)[/tex] by [tex]\(2x^2\)[/tex]:
[tex]\[
9x^2 \times 2x^2 = 18x^{2+2} = 18x^4
\][/tex]
- Finally, multiply [tex]\(9x^2\)[/tex] by [tex]\(-1\)[/tex]:
[tex]\[
9x^2 \times -1 = -9x^2
\][/tex]
2. Combine the terms to get the simplified expression:
[tex]\[
18x^4 + 36x^3 - 9x^2
\][/tex]
So, the correct simplification is [tex]\(18x^4 + 36x^3 - 9x^2\)[/tex], which matches the option: [tex]\(18 x^4 + 36 x^3 - 9 x^2\)[/tex].
We need to simplify the expression [tex]\(9x^2(4x + 2x^2 - 1)\)[/tex].
1. Distribute [tex]\(9x^2\)[/tex] to each term inside the parentheses:
- First, multiply [tex]\(9x^2\)[/tex] by [tex]\(4x\)[/tex]:
[tex]\[
9x^2 \times 4x = 36x^{2+1} = 36x^3
\][/tex]
- Next, multiply [tex]\(9x^2\)[/tex] by [tex]\(2x^2\)[/tex]:
[tex]\[
9x^2 \times 2x^2 = 18x^{2+2} = 18x^4
\][/tex]
- Finally, multiply [tex]\(9x^2\)[/tex] by [tex]\(-1\)[/tex]:
[tex]\[
9x^2 \times -1 = -9x^2
\][/tex]
2. Combine the terms to get the simplified expression:
[tex]\[
18x^4 + 36x^3 - 9x^2
\][/tex]
So, the correct simplification is [tex]\(18x^4 + 36x^3 - 9x^2\)[/tex], which matches the option: [tex]\(18 x^4 + 36 x^3 - 9 x^2\)[/tex].
