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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], 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.

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