Answer :
To simplify the expression [tex]\(9x^2(4x + 2x^2 - 1)\)[/tex], let's break it down step-by-step:
1. Distribute [tex]\(9x^2\)[/tex] to each term inside the parentheses:
[tex]\[
9x^2 \times 4x + 9x^2 \times 2x^2 + 9x^2 \times (-1)
\][/tex]
2. Calculate each multiplication:
- First term: [tex]\(9x^2 \times 4x = 36x^3\)[/tex]
- Second term: [tex]\(9x^2 \times 2x^2 = 18x^4\)[/tex]
- Third term: [tex]\(9x^2 \times (-1) = -9x^2\)[/tex]
3. Combine the terms:
[tex]\[
18x^4 + 36x^3 - 9x^2
\][/tex]
So the correct simplification is [tex]\(18x^4 + 36x^3 - 9x^2\)[/tex]. This matches with one of the options provided, which is the first one.
1. Distribute [tex]\(9x^2\)[/tex] to each term inside the parentheses:
[tex]\[
9x^2 \times 4x + 9x^2 \times 2x^2 + 9x^2 \times (-1)
\][/tex]
2. Calculate each multiplication:
- First term: [tex]\(9x^2 \times 4x = 36x^3\)[/tex]
- Second term: [tex]\(9x^2 \times 2x^2 = 18x^4\)[/tex]
- Third term: [tex]\(9x^2 \times (-1) = -9x^2\)[/tex]
3. Combine the terms:
[tex]\[
18x^4 + 36x^3 - 9x^2
\][/tex]
So the correct simplification is [tex]\(18x^4 + 36x^3 - 9x^2\)[/tex]. This matches with one of the options provided, which is the first one.
