Answer :
To simplify the expression [tex]\( 9x^2(4x + 2x^2 - 1) \)[/tex], we need to distribute [tex]\( 9x^2 \)[/tex] to each term inside the parentheses. Here’s how this can be done step-by-step:
1. Distribute [tex]\( 9x^2 \)[/tex]:
- Multiply [tex]\( 9x^2 \)[/tex] with [tex]\( 4x \)[/tex]:
[tex]\[
9x^2 \times 4x = 36x^3
\][/tex]
- Multiply [tex]\( 9x^2 \)[/tex] with [tex]\( 2x^2 \)[/tex]:
[tex]\[
9x^2 \times 2x^2 = 18x^4
\][/tex]
- Multiply [tex]\( 9x^2 \)[/tex] with [tex]\(-1\)[/tex]:
[tex]\[
9x^2 \times -1 = -9x^2
\][/tex]
2. Combine these results:
Now, combine all the results from the distribution:
[tex]\[
18x^4 + 36x^3 - 9x^2
\][/tex]
Thus, the simplified form of the expression [tex]\( 9x^2(4x + 2x^2 - 1) \)[/tex] is:
[tex]\[ 18x^4 + 36x^3 - 9x^2 \][/tex]
Comparing this with the provided choices, the correct option is:
a) [tex]\( 18x^4 + 36x^3 - 9x^2 \)[/tex]
1. Distribute [tex]\( 9x^2 \)[/tex]:
- Multiply [tex]\( 9x^2 \)[/tex] with [tex]\( 4x \)[/tex]:
[tex]\[
9x^2 \times 4x = 36x^3
\][/tex]
- Multiply [tex]\( 9x^2 \)[/tex] with [tex]\( 2x^2 \)[/tex]:
[tex]\[
9x^2 \times 2x^2 = 18x^4
\][/tex]
- Multiply [tex]\( 9x^2 \)[/tex] with [tex]\(-1\)[/tex]:
[tex]\[
9x^2 \times -1 = -9x^2
\][/tex]
2. Combine these results:
Now, combine all the results from the distribution:
[tex]\[
18x^4 + 36x^3 - 9x^2
\][/tex]
Thus, the simplified form of the expression [tex]\( 9x^2(4x + 2x^2 - 1) \)[/tex] is:
[tex]\[ 18x^4 + 36x^3 - 9x^2 \][/tex]
Comparing this with the provided choices, the correct option is:
a) [tex]\( 18x^4 + 36x^3 - 9x^2 \)[/tex]
