High School

Choose the correct simplification of [tex]$9x^2(4x + 2x^2 - 1)$[/tex].

A. [tex]18x^4 + 36x^3 - 9x^2[/tex]

B. [tex]18x^4 - 36x^3 + 9x^2[/tex]

C. [tex]36x^4 + 18x^3 - 9x^2[/tex]

D. [tex]36x^4 - 13x^3 + 9x^2[/tex]

Answer :

To simplify the expression [tex]\(9x^2(4x + 2x^2 - 1)\)[/tex], follow these steps:

1. Distribute [tex]\(9x^2\)[/tex] across the terms inside the parentheses:

- Multiply [tex]\(9x^2\)[/tex] by [tex]\(4x\)[/tex]:

[tex]\[
9x^2 \cdot 4x = 36x^3
\][/tex]

- Multiply [tex]\(9x^2\)[/tex] by [tex]\(2x^2\)[/tex]:

[tex]\[
9x^2 \cdot 2x^2 = 18x^4
\][/tex]

- Multiply [tex]\(9x^2\)[/tex] by [tex]\(-1\)[/tex]:

[tex]\[
9x^2 \cdot (-1) = -9x^2
\][/tex]

2. Combine all the terms together:

[tex]\[
18x^4 + 36x^3 - 9x^2
\][/tex]

Therefore, the correct simplification of the expression [tex]\(9x^2(4x + 2x^2 - 1)\)[/tex] is:

[tex]\[
\boxed{18x^4 + 36x^3 - 9x^2}
\][/tex]

This matches with the first option listed in your question choices.