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

Question

High School

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Answer :

roniksingha96 roniksingha96 · Answer 1 · 2023-08-25T18:10:10-04:00

The correct simplification would be [tex]18x^4 - 36x^3 + 9x^2[/tex] (option a).

To simplify the expression [tex]9x^2(4x - 2x^2[/tex] - 1), we need to perform the multiplication and combine like terms.

1. Start by distributing the 9x^2 to each term inside the parentheses:

[tex]9x^2 * 4x = 36x^3 9x^2 * (-2x^2) = -18x^4 9x^2 * (-1) = -9x^2[/tex]

2. Now we can combine the terms obtained from the distribution:

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

3. Rearranging the terms in descending order of exponents:

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

4. However, we can simplify this expression further by factoring out a common factor of [tex]-9x^2[/tex]:

[tex]-9x^2(2x^2 - 4x + 1)[/tex]

5. Thus, the final simplified expression is:

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

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