Answer :
Sure, here is the detailed step-by-step solution for simplifying [tex]\( 9 x^2(4 x + 2 x^2 - 1) \)[/tex]:
1. Distribute [tex]\( 9 x^2 \)[/tex] to each term inside the parentheses:
- First, multiply [tex]\( 9 x^2 \)[/tex] by [tex]\( 4 x \)[/tex]:
[tex]\[
9 x^2 \times 4 x = 36 x^3
\][/tex]
- Next, multiply [tex]\( 9 x^2 \)[/tex] by [tex]\( 2 x^2 \)[/tex]:
[tex]\[
9 x^2 \times 2 x^2 = 18 x^4
\][/tex]
- Finally, multiply [tex]\( 9 x^2 \)[/tex] by [tex]\(-1\)[/tex]:
[tex]\[
9 x^2 \times (-1) = -9 x^2
\][/tex]
2. Combine the results from each multiplication:
[tex]\[
18 x^4 + 36 x^3 - 9 x^2
\][/tex]
So, the correct simplification of [tex]\( 9 x^2(4 x + 2 x^2 - 1) \)[/tex] is:
[tex]\[
18 x^4 + 36 x^3 - 9 x^2
\][/tex]
Therefore, the correct choice from the given options is:
[tex]\[
18 x^4 + 36 x^3 - 9 x^2
\][/tex]
1. Distribute [tex]\( 9 x^2 \)[/tex] to each term inside the parentheses:
- First, multiply [tex]\( 9 x^2 \)[/tex] by [tex]\( 4 x \)[/tex]:
[tex]\[
9 x^2 \times 4 x = 36 x^3
\][/tex]
- Next, multiply [tex]\( 9 x^2 \)[/tex] by [tex]\( 2 x^2 \)[/tex]:
[tex]\[
9 x^2 \times 2 x^2 = 18 x^4
\][/tex]
- Finally, multiply [tex]\( 9 x^2 \)[/tex] by [tex]\(-1\)[/tex]:
[tex]\[
9 x^2 \times (-1) = -9 x^2
\][/tex]
2. Combine the results from each multiplication:
[tex]\[
18 x^4 + 36 x^3 - 9 x^2
\][/tex]
So, the correct simplification of [tex]\( 9 x^2(4 x + 2 x^2 - 1) \)[/tex] is:
[tex]\[
18 x^4 + 36 x^3 - 9 x^2
\][/tex]
Therefore, the correct choice from the given options is:
[tex]\[
18 x^4 + 36 x^3 - 9 x^2
\][/tex]
