College

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

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

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

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

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

Answer :

To simplify the expression [tex]\(9x^2(4x + 2x^2 - 1)\)[/tex], let's distribute [tex]\(9x^2\)[/tex] to each term inside the parentheses. Here's the step-by-step process:

1. Distribute [tex]\(9x^2\)[/tex] to each term:

- Multiply [tex]\(9x^2\)[/tex] by [tex]\(4x\)[/tex]:
[tex]\[
9x^2 \times 4x = 36x^3
\][/tex]

- Multiply [tex]\(9x^2\)[/tex] by [tex]\(2x^2\)[/tex]:
[tex]\[
9x^2 \times 2x^2 = 18x^4
\][/tex]

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

2. Combine the results:

Now, write the expression with all terms:
[tex]\[
18x^4 + 36x^3 - 9x^2
\][/tex]

So, the correct simplification of [tex]\(9x^2(4x + 2x^2 - 1)\)[/tex] is:
[tex]\[
18x^4 + 36x^3 - 9x^2
\][/tex]

This matches the first option in the given choices.

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