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Answer :
Let's simplify the expression [tex]\(3 x^2 (7 x^2 - 3)\)[/tex] step-by-step.
1. Distribute [tex]\(3 x^2\)[/tex] across the terms inside the parenthesis:
- Multiply [tex]\(3 x^2\)[/tex] by [tex]\(7 x^2\)[/tex]:
[tex]\[
3 x^2 \times 7 x^2 = 21 x^4
\][/tex]
- Multiply [tex]\(3 x^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
3 x^2 \times (-3) = -9 x^2
\][/tex]
2. Combine the results:
When we distribute and combine the results, the expression becomes:
[tex]\[
21 x^4 - 9 x^2
\][/tex]
Now, let's match this with one of the given options:
- A. [tex]\(21 x^2 - 3\)[/tex]
- B. [tex]\(21 x^2 - 27 x^2\)[/tex]
- C. [tex]\(21 x^4 - 9\)[/tex]
- D. [tex]\(21 x^4 - 27 x^2\)[/tex]
The correct simplified expression is [tex]\(21 x^4 - 9 x^2\)[/tex].
However, it seems the available choices do not perfectly match this result. The closest simplification from the choices is not directly listed. Therefore, if we refer closely to option C, [tex]\(21 x^4 - 9\)[/tex], it seems like there's a resemblance except for the term involving [tex]\( x^2 \)[/tex].
Therefore, if there was a mistake in reading or writing options, or if there was a more filled context, then a close potential match seems to be C, but with the context it was presented, the typical match should involve some common terms with [tex]\(x^2\)[/tex]. Let's affirm that the derived form closest to the context description fits our breakdown as [tex]\(21x^4 - 9x^2\)[/tex] in potential context provision with a needful correction return.
1. Distribute [tex]\(3 x^2\)[/tex] across the terms inside the parenthesis:
- Multiply [tex]\(3 x^2\)[/tex] by [tex]\(7 x^2\)[/tex]:
[tex]\[
3 x^2 \times 7 x^2 = 21 x^4
\][/tex]
- Multiply [tex]\(3 x^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
3 x^2 \times (-3) = -9 x^2
\][/tex]
2. Combine the results:
When we distribute and combine the results, the expression becomes:
[tex]\[
21 x^4 - 9 x^2
\][/tex]
Now, let's match this with one of the given options:
- A. [tex]\(21 x^2 - 3\)[/tex]
- B. [tex]\(21 x^2 - 27 x^2\)[/tex]
- C. [tex]\(21 x^4 - 9\)[/tex]
- D. [tex]\(21 x^4 - 27 x^2\)[/tex]
The correct simplified expression is [tex]\(21 x^4 - 9 x^2\)[/tex].
However, it seems the available choices do not perfectly match this result. The closest simplification from the choices is not directly listed. Therefore, if we refer closely to option C, [tex]\(21 x^4 - 9\)[/tex], it seems like there's a resemblance except for the term involving [tex]\( x^2 \)[/tex].
Therefore, if there was a mistake in reading or writing options, or if there was a more filled context, then a close potential match seems to be C, but with the context it was presented, the typical match should involve some common terms with [tex]\(x^2\)[/tex]. Let's affirm that the derived form closest to the context description fits our breakdown as [tex]\(21x^4 - 9x^2\)[/tex] in potential context provision with a needful correction return.
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