High School

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ 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.